Sanders, Sam Representations and the foundations of mathematics. (English) Zbl 07522852 Notre Dame J. Formal Logic 63, No. 1, 1-28 (2022). MSC: 03B30 03F35 PDF BibTeX XML Cite \textit{S. Sanders}, Notre Dame J. Formal Logic 63, No. 1, 1--28 (2022; Zbl 07522852) Full Text: DOI OpenURL
Barrett, Jordan Mitchell; Downey, Rodney G.; Greenberg, Noam Cousin’s lemma in second-order arithmetic. (English) Zbl 07514667 Proc. Am. Math. Soc., Ser. B 9, 111-124 (2022). MSC: 03B30 03F35 03D78 26A39 PDF BibTeX XML Cite \textit{J. M. Barrett} et al., Proc. Am. Math. Soc., Ser. B 9, 111--124 (2022; Zbl 07514667) Full Text: DOI OpenURL
Freund, Anton; Rathjen, Michael; Weiermann, Andreas Minimal bad sequences are necessary for a uniform Kruskal theorem. (English) Zbl 07507731 Adv. Math. 400, Article ID 108265, 44 p. (2022). MSC: 03B30 05C05 06A07 68Q42 03F35 PDF BibTeX XML Cite \textit{A. Freund} et al., Adv. Math. 400, Article ID 108265, 44 p. (2022; Zbl 07507731) Full Text: DOI OpenURL
Liu, Lu; Patey, Ludovic The reverse mathematics of the thin set and Erdős-Moser theorems. (English) Zbl 07506780 J. Symb. Log. 87, No. 1, 313-346 (2022). MSC: 03D80 03F35 03B30 PDF BibTeX XML Cite \textit{L. Liu} and \textit{L. Patey}, J. Symb. Log. 87, No. 1, 313--346 (2022; Zbl 07506780) Full Text: DOI OpenURL
Barnes, James S.; Goh, Jun Le; Shore, Richard A. Theorems of hyperarithmetic analysis and almost theorems of hyperarithmetic analysis. (English) Zbl 07503072 Bull. Symb. Log. 28, No. 1, 133-149 (2022). MSC: 03B30 03D55 03F35 05C63 03D80 05C38 05C69 05C70 PDF BibTeX XML Cite \textit{J. S. Barnes} et al., Bull. Symb. Log. 28, No. 1, 133--149 (2022; Zbl 07503072) Full Text: DOI OpenURL
Kurahashi, Taishi; Okawa, Yuya; Shavrukov, V. Yu.; Visser, Albert On Guaspari’s problem about partially conservative sentences. (English) Zbl 07501982 Ann. Pure Appl. Logic 173, No. 5, Article ID 103087, 25 p. (2022). MSC: 03F40 03F30 03F03 03F99 PDF BibTeX XML Cite \textit{T. Kurahashi} et al., Ann. Pure Appl. Logic 173, No. 5, Article ID 103087, 25 p. (2022; Zbl 07501982) Full Text: DOI OpenURL
Jeon, Hanul Constructive Ackermann’s interpretation. (English) Zbl 07501981 Ann. Pure Appl. Logic 173, No. 5, Article ID 103086, 19 p. (2022). MSC: 03F50 03E70 03F30 03F65 PDF BibTeX XML Cite \textit{H. Jeon}, Ann. Pure Appl. Logic 173, No. 5, Article ID 103086, 19 p. (2022; Zbl 07501981) Full Text: DOI OpenURL
Adamowicz, Zofia Restricted polynomial induction versus parameter free ordinary induction. (English) Zbl 07499607 Fundam. Math. 257, No. 2, 167-187 (2022). MSC: 03F30 03F40 PDF BibTeX XML Cite \textit{Z. Adamowicz}, Fundam. Math. 257, No. 2, 167--187 (2022; Zbl 07499607) Full Text: DOI OpenURL
Fiori-Carones, Marta; Shafer, Paul; Soldà, Giovanni An inside/outside Ramsey theorem and recursion theory. (English) Zbl 07479592 Trans. Am. Math. Soc. 375, No. 3, 1977-2024 (2022). MSC: 03B30 03D30 03F35 PDF BibTeX XML Cite \textit{M. Fiori-Carones} et al., Trans. Am. Math. Soc. 375, No. 3, 1977--2024 (2022; Zbl 07479592) Full Text: DOI arXiv OpenURL
Dzhafarov, Damir; Flood, Stephen; Solomon, Reed; Westrick, Linda Effectiveness for the dual Ramsey theorem. (English) Zbl 07473054 Notre Dame J. Formal Logic 62, No. 3, 455-490 (2021). MSC: 03D80 05C55 03F60 03F35 03B30 PDF BibTeX XML Cite \textit{D. Dzhafarov} et al., Notre Dame J. Formal Logic 62, No. 3, 455--490 (2021; Zbl 07473054) Full Text: DOI arXiv OpenURL
Leivant, Daniel Finitism, imperative programs and primitive recursion. (English) Zbl 07471465 J. Log. Comput. 31, No. 1, 179-192 (2021). MSC: 03D20 03F30 03A05 PDF BibTeX XML Cite \textit{D. Leivant}, J. Log. Comput. 31, No. 1, 179--192 (2021; Zbl 07471465) Full Text: DOI OpenURL
Blanck, Rasmus Hierarchical incompleteness results for arithmetically definable extensions of fragments of arithmetic. (English) Zbl 07464264 Rev. Symb. Log. 14, No. 3, 624-644 (2021). MSC: 03F25 03F30 03F40 03H15 PDF BibTeX XML Cite \textit{R. Blanck}, Rev. Symb. Log. 14, No. 3, 624--644 (2021; Zbl 07464264) Full Text: DOI arXiv OpenURL
Kossak, Roman; Wcisło, Bartosz Disjunctions with stopping conditions. (English) Zbl 07455123 Bull. Symb. Log. 27, No. 3, 231-253 (2021). MSC: 03H15 03F30 03A99 PDF BibTeX XML Cite \textit{R. Kossak} and \textit{B. Wcisło}, Bull. Symb. Log. 27, No. 3, 231--253 (2021; Zbl 07455123) Full Text: DOI arXiv OpenURL
Meyer, Robert K. The consistency of arithmetic. (English) Zbl 07451166 Australas. J. Log. 18, No. 5, 289-379 (2021). Reviewer: Lukasz Stepien (Kraków) MSC: 03F30 03F40 PDF BibTeX XML Cite \textit{R. K. Meyer}, Australas. J. Log. 18, No. 5, 289--379 (2021; Zbl 07451166) Full Text: DOI OpenURL
Fujiwara, Makoto; Kurahashi, Taishi Prenex normal form theorems in semi-classical arithmetic. (English) Zbl 07442022 J. Symb. Log. 86, No. 3, 1124-1153 (2021). MSC: 03B20 03F03 03F30 03F50 PDF BibTeX XML Cite \textit{M. Fujiwara} and \textit{T. Kurahashi}, J. Symb. Log. 86, No. 3, 1124--1153 (2021; Zbl 07442022) Full Text: DOI arXiv OpenURL
Monin, Benoit; Patey, Ludovic The weakness of the pigeonhole principle under hyperarithmetical reductions. (English) Zbl 07419663 J. Math. Log. 21, No. 3, Article ID 2150013, 41 p. (2021). MSC: 03B30 03F35 PDF BibTeX XML Cite \textit{B. Monin} and \textit{L. Patey}, J. Math. Log. 21, No. 3, Article ID 2150013, 41 p. (2021; Zbl 07419663) Full Text: DOI arXiv OpenURL
Ferreira, Fernando The abstract type of the real numbers. (English) Zbl 07417496 Arch. Math. Logic 60, No. 7-8, 1005-1017 (2021). Reviewer: Jeffry L. Hirst (Boone) MSC: 03B30 03F35 03F10 54F15 PDF BibTeX XML Cite \textit{F. Ferreira}, Arch. Math. Logic 60, No. 7--8, 1005--1017 (2021; Zbl 07417496) Full Text: DOI OpenURL
Freund, Anton Well ordering principles and \(\Pi^1_4\)-statements: a pilot study. (English) Zbl 07415222 J. Symb. Log. 86, No. 2, 709-745 (2021). Reviewer: Jeffry L. Hirst (Boone) MSC: 03B30 03D65 03F15 03F35 PDF BibTeX XML Cite \textit{A. Freund}, J. Symb. Log. 86, No. 2, 709--745 (2021; Zbl 07415222) Full Text: DOI arXiv OpenURL
Belanger, David; Chong, C. T.; Wang, Wei; Wong, Tin Lok; Yang, Yue Where pigeonhole principles meet König lemmas. (English) Zbl 07412277 Trans. Am. Math. Soc. 374, No. 11, 8275-8303 (2021). MSC: 03B30 03F35 03F30 03D32 PDF BibTeX XML Cite \textit{D. Belanger} et al., Trans. Am. Math. Soc. 374, No. 11, 8275--8303 (2021; Zbl 07412277) Full Text: DOI arXiv OpenURL
Fiori-Carones, Marta; Kołodziejczyk, Leszek Aleksander; Kowalik, Katarzyna W. Weaker cousins of Ramsey’s theorem over a weak base theory. (English) Zbl 07404819 Ann. Pure Appl. Logic 172, No. 10, Article ID 103028, 22 p. (2021). MSC: 03B30 03F30 03F35 03H15 05D10 PDF BibTeX XML Cite \textit{M. Fiori-Carones} et al., Ann. Pure Appl. Logic 172, No. 10, Article ID 103028, 22 p. (2021; Zbl 07404819) Full Text: DOI arXiv OpenURL
Arai, Toshiyasu; Wainer, Stanley S.; Weiermann, Andreas Goodstein sequences based on a parametrized Ackermann-Péter function. (English) Zbl 07396324 Bull. Symb. Log. 27, No. 2, 168-186 (2021). MSC: 03F15 03F25 03F30 03F35 03D55 PDF BibTeX XML Cite \textit{T. Arai} et al., Bull. Symb. Log. 27, No. 2, 168--186 (2021; Zbl 07396324) Full Text: DOI OpenURL
Cheng, Yong Current research on Gödel’s incompleteness theorems. (English) Zbl 07396323 Bull. Symb. Log. 27, No. 2, 113-167 (2021). Reviewer: Saeed Salehi (Tabriz) MSC: 03F40 03F30 03-02 PDF BibTeX XML Cite \textit{Y. Cheng}, Bull. Symb. Log. 27, No. 2, 113--167 (2021; Zbl 07396323) Full Text: DOI arXiv OpenURL
Monin, Benoit; Patey, Ludovic \( \mathsf{SRT}_2^2\) does not imply \(\mathsf{RT}_2^2\) in \(\omega \)-models. (English) Zbl 07384219 Adv. Math. 389, Article ID 107903, 32 p. (2021). MSC: 03B30 03F35 PDF BibTeX XML Cite \textit{B. Monin} and \textit{L. Patey}, Adv. Math. 389, Article ID 107903, 32 p. (2021; Zbl 07384219) Full Text: DOI arXiv OpenURL
Chong, Chi Tat; Li, Wei; Liu, Lu; Yang, Yue The strength of Ramsey’s theorem for pairs over trees. I: Weak König’s lemma. (English) Zbl 07377373 Trans. Am. Math. Soc. 374, No. 8, 5545-5581 (2021). Reviewer: Jeffry L. Hirst (Boone) MSC: 03B30 03F35 03D80 05D10 PDF BibTeX XML Cite \textit{C. T. Chong} et al., Trans. Am. Math. Soc. 374, No. 8, 5545--5581 (2021; Zbl 07377373) Full Text: DOI arXiv OpenURL
Grabmayr, Balthasar On the invariance of Gödel’s second theorem with regard to numberings. (English) Zbl 07374090 Rev. Symb. Log. 14, No. 1, 51-84 (2021). Reviewer: Saeed Salehi (Tabriz) MSC: 03A05 03B25 03F30 03F40 PDF BibTeX XML Cite \textit{B. Grabmayr}, Rev. Symb. Log. 14, No. 1, 51--84 (2021; Zbl 07374090) Full Text: DOI arXiv OpenURL
Lutz, Patrick; Walsh, James Corrigenda to: “Incompleteness and jump hierarchies”. (English) Zbl 1473.03023 Proc. Am. Math. Soc. 149, No. 7, 3143-3144 (2021). MSC: 03D55 03F35 03F40 PDF BibTeX XML Cite \textit{P. Lutz} and \textit{J. Walsh}, Proc. Am. Math. Soc. 149, No. 7, 3143--3144 (2021; Zbl 1473.03023) Full Text: DOI OpenURL
Visser, Albert The absorption law. Or: how to Kreisel a Hilbert-Bernays-Löb. (English) Zbl 07334540 Arch. Math. Logic 60, No. 3-4, 441-468 (2021). MSC: 03F30 03F40 03F45 PDF BibTeX XML Cite \textit{A. Visser}, Arch. Math. Logic 60, No. 3--4, 441--468 (2021; Zbl 07334540) Full Text: DOI arXiv OpenURL
Łełyk, Mateusz; Wcisło, Bartosz Local collection and end-extensions of models of compositional truth. (English) Zbl 1473.03047 Ann. Pure Appl. Logic 172, No. 6, Article ID 102941, 22 p. (2021). Reviewer: Roman Kossak (New York) MSC: 03H15 03F30 03C62 03A05 PDF BibTeX XML Cite \textit{M. Łełyk} and \textit{B. Wcisło}, Ann. Pure Appl. Logic 172, No. 6, Article ID 102941, 22 p. (2021; Zbl 1473.03047) Full Text: DOI arXiv OpenURL
Dinis, Bruno; Oliva, Paulo A parametrised functional interpretation of Heyting arithmetic. (English) Zbl 07327747 Ann. Pure Appl. Logic 172, No. 4, Article ID 102940, 24 p. (2021). MSC: 03F07 03F10 03F30 03F55 PDF BibTeX XML Cite \textit{B. Dinis} and \textit{P. Oliva}, Ann. Pure Appl. Logic 172, No. 4, Article ID 102940, 24 p. (2021; Zbl 07327747) Full Text: DOI OpenURL
Enayat, Ali; Schmerl, James H. The Barwise-Schlipf theorem. (English) Zbl 1459.03049 Proc. Am. Math. Soc. 149, No. 1, 413-416 (2021). Reviewer: Roman Kossak (New York) MSC: 03C62 03C50 03H15 PDF BibTeX XML Cite \textit{A. Enayat} and \textit{J. H. Schmerl}, Proc. Am. Math. Soc. 149, No. 1, 413--416 (2021; Zbl 1459.03049) Full Text: DOI arXiv OpenURL
Brattka, Vasco; Gherardi, Guido Completion of choice. (English) Zbl 1462.03019 Ann. Pure Appl. Logic 172, No. 3, Article ID 102914, 31 p. (2021). Reviewer: Jeffry L. Hirst (Boone) MSC: 03D78 03B30 03D30 03F60 03F35 PDF BibTeX XML Cite \textit{V. Brattka} and \textit{G. Gherardi}, Ann. Pure Appl. Logic 172, No. 3, Article ID 102914, 31 p. (2021; Zbl 1462.03019) Full Text: DOI arXiv OpenURL
Fujiwara, Makoto; Kawai, Tatsuji Characterising Brouwer’s continuity by bar recursion on moduli of continuity. (English) Zbl 07297808 Arch. Math. Logic 60, No. 1-2, 241-263 (2021). MSC: 03F55 03F35 03F50 03F10 PDF BibTeX XML Cite \textit{M. Fujiwara} and \textit{T. Kawai}, Arch. Math. Logic 60, No. 1--2, 241--263 (2021; Zbl 07297808) Full Text: DOI OpenURL
Pianigiani, Duccio; Sorbi, Andrea A note on uniform density in weak arithmetical theories. (English) Zbl 1477.03170 Arch. Math. Logic 60, No. 1-2, 211-225 (2021). Reviewer: Leszek Aleksander Kołodziejczyk (Warszawa) MSC: 03D45 03F30 03F55 PDF BibTeX XML Cite \textit{D. Pianigiani} and \textit{A. Sorbi}, Arch. Math. Logic 60, No. 1--2, 211--225 (2021; Zbl 1477.03170) Full Text: DOI OpenURL
Wu, Huishan Ring structure theorems and arithmetic comprehension. (English) Zbl 1473.03009 Arch. Math. Logic 60, No. 1-2, 145-160 (2021). Reviewer: Jeffry L. Hirst (Boone) MSC: 03B30 03D15 03F35 03D80 13E10 PDF BibTeX XML Cite \textit{H. Wu}, Arch. Math. Logic 60, No. 1--2, 145--160 (2021; Zbl 1473.03009) Full Text: DOI OpenURL
Freund, Anton; Rathjen, Michael Derivatives of normal functions in reverse mathematics. (English) Zbl 1473.03036 Ann. Pure Appl. Logic 172, No. 2, Article ID 102890, 50 p. (2021). Reviewer: Andrei Sipoş (Bucureşti) MSC: 03F15 03B30 03F35 03D60 03E10 PDF BibTeX XML Cite \textit{A. Freund} and \textit{M. Rathjen}, Ann. Pure Appl. Logic 172, No. 2, Article ID 102890, 50 p. (2021; Zbl 1473.03036) Full Text: DOI arXiv OpenURL
Yan, Shaodan; Zhao, Fengqun; Li, Can; Zhao, Le High order WSGL difference operators combined with Sinc-Galerkin method for time fractional Schrödinger equation. (English) Zbl 07476506 Int. J. Comput. Math. 97, No. 11, 2259-2286 (2020). MSC: 26A33 03F35 47B37 65M12 PDF BibTeX XML Cite \textit{S. Yan} et al., Int. J. Comput. Math. 97, No. 11, 2259--2286 (2020; Zbl 07476506) Full Text: DOI OpenURL
Rathjen, Michael; Thomson, Ian Alexander Well-ordering principles, \( \omega \)-models and \(\prod_1^1 \)-comprehension. (English) Zbl 07438596 Kahle, Reinhard (ed.) et al., The legacy of Kurt Schütte. Cham: Springer. 171-215 (2020). MSC: 03B30 03F05 03F15 03F35 03F35 PDF BibTeX XML Cite \textit{M. Rathjen} and \textit{I. A. Thomson}, in: The legacy of Kurt Schütte. Cham: Springer. 171--215 (2020; Zbl 07438596) Full Text: DOI OpenURL
Sanders, Sam Reverse mathematics of topology: dimension, paracompactness, and splittings. (English) Zbl 07391957 Notre Dame J. Formal Logic 61, No. 4, 537-559 (2020). MSC: 03B30 03F35 PDF BibTeX XML Cite \textit{S. Sanders}, Notre Dame J. Formal Logic 61, No. 4, 537--559 (2020; Zbl 07391957) Full Text: DOI arXiv OpenURL
Ferreira, Fernando Weak König’s lemma in herbrandized classical second-order arithmetic. (English) Zbl 07376806 Port. Math. (N.S.) 77, No. 3-4, 399-408 (2020). MSC: 03F10 03B30 03F35 PDF BibTeX XML Cite \textit{F. Ferreira}, Port. Math. (N.S.) 77, No. 3--4, 399--408 (2020; Zbl 07376806) Full Text: DOI OpenURL
Towsner, Henry Constructing sequences one step at a time. (English) Zbl 07349733 J. Math. Log. 20, No. 3, Article ID 2050017, 43 p. (2020). MSC: 03B30 03F35 PDF BibTeX XML Cite \textit{H. Towsner}, J. Math. Log. 20, No. 3, Article ID 2050017, 43 p. (2020; Zbl 07349733) Full Text: DOI arXiv OpenURL
Ferreira, Fernando Bounds for indexes of nilpotency in commutative ring theory: a proof mining approach. (English) Zbl 1462.03025 Bull. Symb. Log. 26, No. 3-4, 257-267 (2020). Reviewer: Victor V. Pambuccian (Glendale) MSC: 03F10 13A15 13F20 03F35 PDF BibTeX XML Cite \textit{F. Ferreira}, Bull. Symb. Log. 26, No. 3--4, 257--267 (2020; Zbl 1462.03025) Full Text: DOI OpenURL
Cheng, Yong Finding the limit of incompleteness. I. (English) Zbl 1464.03089 Bull. Symb. Log. 26, No. 3-4, 268-286 (2020). Reviewer: Saeed Salehi (Tabriz) MSC: 03F40 03F30 03D35 PDF BibTeX XML Cite \textit{Y. Cheng}, Bull. Symb. Log. 26, No. 3--4, 268--286 (2020; Zbl 1464.03089) Full Text: DOI arXiv OpenURL
Salehi, Saeed Gödel’s second incompleteness theorem: how it is derived and what it delivers. (English) Zbl 1462.03026 Bull. Symb. Log. 26, No. 3-4, 241-256 (2020). Reviewer: Roman Murawski (Poznań) MSC: 03F40 03F30 03D32 PDF BibTeX XML Cite \textit{S. Salehi}, Bull. Symb. Log. 26, No. 3--4, 241--256 (2020; Zbl 1462.03026) Full Text: DOI OpenURL
Kurahashi, Taishi A note on derivability conditions. (English) Zbl 1473.03037 J. Symb. Log. 85, No. 3, 1224-1253 (2020). Reviewer: Saeed Salehi (Tabriz) MSC: 03F30 03F40 PDF BibTeX XML Cite \textit{T. Kurahashi}, J. Symb. Log. 85, No. 3, 1224--1253 (2020; Zbl 1473.03037) Full Text: DOI arXiv OpenURL
Kihara, Takayuki; Marcone, Alberto; Pauly, Arno Searching for an analogue of \(\text{ATR}_0\) in the Weihrauch lattice. (English) Zbl 1473.03026 J. Symb. Log. 85, No. 3, 1006-1043 (2020). Reviewer: Jeffry L. Hirst (Boone) MSC: 03D78 03D30 03B30 03F35 PDF BibTeX XML Cite \textit{T. Kihara} et al., J. Symb. Log. 85, No. 3, 1006--1043 (2020; Zbl 1473.03026) Full Text: DOI arXiv OpenURL
Freund, Anton How strong are single fixed points of normal functions? (English) Zbl 1462.03008 J. Symb. Log. 85, No. 2, 709-732 (2020). Reviewer: Jeffry L. Hirst (Boone) MSC: 03B30 03F15 03F35 PDF BibTeX XML Cite \textit{A. Freund}, J. Symb. Log. 85, No. 2, 709--732 (2020; Zbl 1462.03008) Full Text: DOI arXiv OpenURL
Salehi, Saeed On the diagonal lemma of Gödel and Carnap. (English) Zbl 1459.03089 Bull. Symb. Log. 26, No. 1, 80-88 (2020). Reviewer: Victor V. Pambuccian (Glendale) MSC: 03F40 03F30 PDF BibTeX XML Cite \textit{S. Salehi}, Bull. Symb. Log. 26, No. 1, 80--88 (2020; Zbl 1459.03089) Full Text: DOI OpenURL
Normann, Dag; Sanders, Sam Open sets in computability theory and reverse mathematics. (English) Zbl 1472.03012 J. Log. Comput. 30, No. 8, 1639-1679 (2020). Reviewer: Jeffry L. Hirst (Boone) MSC: 03B30 03D65 03F35 03D80 03F60 PDF BibTeX XML Cite \textit{D. Normann} and \textit{S. Sanders}, J. Log. Comput. 30, No. 8, 1639--1679 (2020; Zbl 1472.03012) Full Text: DOI arXiv OpenURL
Hirst, Jeffry L. Leaf management. (English) Zbl 07271577 Computability 9, No. 3-4, 309-314 (2020). MSC: 03F35 03B30 03D30 PDF BibTeX XML Cite \textit{J. L. Hirst}, Computability 9, No. 3--4, 309--314 (2020; Zbl 07271577) Full Text: DOI arXiv OpenURL
Davis, Caleb; Hirschfeldt, Denis R.; Hirst, Jeffry; Pardo, Jake; Pauly, Arno; Yokoyama, Keita Combinatorial principles equivalent to weak induction. (English) Zbl 07271574 Computability 9, No. 3-4, 219-229 (2020). MSC: 03B30 03D30 03F35 05D10 PDF BibTeX XML Cite \textit{C. Davis} et al., Computability 9, No. 3--4, 219--229 (2020; Zbl 07271574) Full Text: DOI arXiv OpenURL
Cholak, Peter A.; Dzhafarov, Damir D.; Hirschfeldt, Denis R.; Patey, Ludovic Some results concerning the \(\mathsf{SRT}_2^2\) vs. \(\mathsf{COH}\) problem. (English) Zbl 07271573 Computability 9, No. 3-4, 193-217 (2020). MSC: 03B30 03F35 05D10 PDF BibTeX XML Cite \textit{P. A. Cholak} et al., Computability 9, No. 3--4, 193--217 (2020; Zbl 07271573) Full Text: DOI arXiv OpenURL
Dudakov, S. M. On undecidability of concatenation theory for one-symbol languages. (English) Zbl 07266240 Lobachevskii J. Math. 41, No. 2, 168-175 (2020). MSC: 03D35 03B25 03F30 03F35 PDF BibTeX XML Cite \textit{S. M. Dudakov}, Lobachevskii J. Math. 41, No. 2, 168--175 (2020; Zbl 07266240) Full Text: DOI OpenURL
Kolmakov, Evgeny Local reflection, definable elements and 1-provability. (English) Zbl 07261478 Arch. Math. Logic 59, No. 7-8, 979-996 (2020). MSC: 03F30 03C62 PDF BibTeX XML Cite \textit{E. Kolmakov}, Arch. Math. Logic 59, No. 7--8, 979--996 (2020; Zbl 07261478) Full Text: DOI arXiv OpenURL
Bahrami, Saeideh Tanaka’s theorem revisited. (English) Zbl 1461.03055 Arch. Math. Logic 59, No. 7-8, 865-877 (2020). Reviewer: Roman Kossak (New York) MSC: 03F35 03C62 03H15 03C15 PDF BibTeX XML Cite \textit{S. Bahrami}, Arch. Math. Logic 59, No. 7--8, 865--877 (2020; Zbl 1461.03055) Full Text: DOI arXiv OpenURL
Dimitracopoulos, C.; Paschalis, V. End extensions of models of fragments of \(\mathrm{PA}\). (English) Zbl 1459.03048 Arch. Math. Logic 59, No. 7-8, 817-833 (2020). Reviewer: Roman Kossak (New York) MSC: 03C62 03F30 03H15 PDF BibTeX XML Cite \textit{C. Dimitracopoulos} and \textit{V. Paschalis}, Arch. Math. Logic 59, No. 7--8, 817--833 (2020; Zbl 1459.03048) Full Text: DOI OpenURL
Fernández-Duque, David; Shafer, Paul; Yokoyama, Keita Ekeland’s variational principle in weak and strong systems of arithmetic. (English) Zbl 1467.03006 Sel. Math., New Ser. 26, No. 5, Paper No. 68, 37 p. (2020). Reviewer: Anton Freund (Darmstadt) MSC: 03B30 03F35 03F60 58E30 PDF BibTeX XML Cite \textit{D. Fernández-Duque} et al., Sel. Math., New Ser. 26, No. 5, Paper No. 68, 37 p. (2020; Zbl 1467.03006) Full Text: DOI arXiv OpenURL
Salehi, Saeed On rudimentarity, primitive recursivity and representability. (English) Zbl 1472.03067 Rep. Math. Logic 55, 73-85 (2020). Reviewer: Victor V. Pambuccian (Glendale) MSC: 03F40 03D20 03F30 PDF BibTeX XML Cite \textit{S. Salehi}, Rep. Math. Logic 55, 73--85 (2020; Zbl 1472.03067) Full Text: DOI arXiv OpenURL
Warren, Jared Shadows of syntax. Revitalizing logical and mathematical conventionalism. (English) Zbl 07247163 New York, NY: Oxford University Press (ISBN 978-0-19-008615-2/hbk; 978-0-19-008616-9/ebook). xx, 385 p. (2020). MSC: 03-02 03A05 03F30 03H15 03F25 00A30 PDF BibTeX XML Cite \textit{J. Warren}, Shadows of syntax. Revitalizing logical and mathematical conventionalism. New York, NY: Oxford University Press (2020; Zbl 07247163) Full Text: DOI OpenURL
Lutz, Patrick; Walsh, James Incompleteness and jump hierarchies. (English) Zbl 1472.03040 Proc. Am. Math. Soc. 148, No. 11, 4997-5006 (2020); corrigendum ibid. 149, No. 7, 3143-3144 (2021). Reviewer: Roman Murawski (Poznań) MSC: 03D55 03F35 03F40 PDF BibTeX XML Cite \textit{P. Lutz} and \textit{J. Walsh}, Proc. Am. Math. Soc. 148, No. 11, 4997--5006 (2020; Zbl 1472.03040) Full Text: DOI arXiv OpenURL
Ferreira, Fernando The FAN principle and weak König’s lemma in Herbrandized second-order arithmetic. (English) Zbl 1455.03077 Ann. Pure Appl. Logic 171, No. 9, Article ID 102843, 20 p. (2020). Reviewer: Bruno Dinis (Lisboa) MSC: 03F10 03F35 03F50 03B40 03F25 PDF BibTeX XML Cite \textit{F. Ferreira}, Ann. Pure Appl. Logic 171, No. 9, Article ID 102843, 20 p. (2020; Zbl 1455.03077) Full Text: DOI OpenURL
Dean, Walter Incompleteness via paradox and completeness. (English) Zbl 07239857 Rev. Symb. Log. 13, No. 3, 541-592 (2020). MSC: 03F40 03F30 03C62 03H15 03A05 PDF BibTeX XML Cite \textit{W. Dean}, Rev. Symb. Log. 13, No. 3, 541--592 (2020; Zbl 07239857) Full Text: DOI OpenURL
Kushida, Hirohiko A proof theory for the logic of provability in true arithmetic. (English) Zbl 1462.03027 Stud. Log. 108, No. 4, 857-875 (2020). Reviewer: Mladen Vuković (Zagreb) MSC: 03F45 03B45 03F05 03F30 PDF BibTeX XML Cite \textit{H. Kushida}, Stud. Log. 108, No. 4, 857--875 (2020; Zbl 1462.03027) Full Text: DOI OpenURL
McCarty, Charles Satisfiability is false intuitionistically: a question from Dana Scott. (English) Zbl 07239284 Stud. Log. 108, No. 4, 803-813 (2020). MSC: 03F55 03B20 03F35 PDF BibTeX XML Cite \textit{C. McCarty}, Stud. Log. 108, No. 4, 803--813 (2020; Zbl 07239284) Full Text: DOI OpenURL
Kołodziejczyk, Leszek Aleksander; Yokoyama, Keita Some upper bounds on ordinal-valued Ramsey numbers for colourings of pairs. (English) Zbl 1479.05349 Sel. Math., New Ser. 26, No. 4, Paper No. 56, 18 p. (2020). Reviewer: Tyros Konstantinos (Athína) MSC: 05D10 05C55 03F30 03F35 03B30 PDF BibTeX XML Cite \textit{L. A. Kołodziejczyk} and \textit{K. Yokoyama}, Sel. Math., New Ser. 26, No. 4, Paper No. 56, 18 p. (2020; Zbl 1479.05349) Full Text: DOI arXiv OpenURL
Nemoto, Takako Finite sets and infinite sets in weak intuitionistic arithmetic. (English) Zbl 1481.03066 Arch. Math. Logic 59, No. 5-6, 607-657 (2020). MSC: 03F50 03F30 PDF BibTeX XML Cite \textit{T. Nemoto}, Arch. Math. Logic 59, No. 5--6, 607--657 (2020; Zbl 1481.03066) Full Text: DOI OpenURL
Kindvall Gorbow, Paul Rank-initial embeddings of non-standard models of set theory. (English) Zbl 1481.03021 Arch. Math. Logic 59, No. 5-6, 517-563 (2020). MSC: 03C62 03E30 03C15 03C20 03E55 PDF BibTeX XML Cite \textit{P. Kindvall Gorbow}, Arch. Math. Logic 59, No. 5--6, 517--563 (2020; Zbl 1481.03021) Full Text: DOI arXiv OpenURL
Picollo, Lavinia Alethic reference. (English) Zbl 07218658 J. Philos. Log. 49, No. 3, 417-438 (2020). MSC: 03F40 03A05 03F30 PDF BibTeX XML Cite \textit{L. Picollo}, J. Philos. Log. 49, No. 3, 417--438 (2020; Zbl 07218658) Full Text: DOI OpenURL
Jeřábek, Emil Recursive functions and existentially closed structures. (English) Zbl 07215221 J. Math. Log. 20, No. 1, Article ID 2050002, 52 p. (2020). MSC: 03F40 03C45 03F30 03C10 PDF BibTeX XML Cite \textit{E. Jeřábek}, J. Math. Log. 20, No. 1, Article ID 2050002, 52 p. (2020; Zbl 07215221) Full Text: DOI arXiv OpenURL
Arai, Toshiyasu; Fernández-Duque, David; Wainer, Stanley; Weiermann, Andreas Predicatively unprovable termination of the Ackermannian Goodstein process. (English) Zbl 07211082 Proc. Am. Math. Soc. 148, No. 8, 3567-3582 (2020). MSC: 03F40 03D20 03D60 03F30 PDF BibTeX XML Cite \textit{T. Arai} et al., Proc. Am. Math. Soc. 148, No. 8, 3567--3582 (2020; Zbl 07211082) Full Text: DOI arXiv OpenURL
Buss, Sam; Kabanets, Valentine; Kolokolova, Antonina; Koucký, Michal Expander construction in \(\mathrm{VNC}^1\). (English) Zbl 1481.03065 Ann. Pure Appl. Logic 171, No. 7, Article ID 102796, 39 p. (2020). MSC: 03F20 03F30 68Q25 03B05 03D15 PDF BibTeX XML Cite \textit{S. Buss} et al., Ann. Pure Appl. Logic 171, No. 7, Article ID 102796, 39 p. (2020; Zbl 1481.03065) Full Text: DOI OpenURL
Chong, C. T.; Li, Wei; Wang, Wei; Yang, Yue On the strength of Ramsey’s theorem for trees. (English) Zbl 1444.03012 Adv. Math. 369, Article ID 107180, 38 p. (2020). Reviewer: Jeffry L. Hirst (Boone) MSC: 03B30 03F35 03D80 05D10 PDF BibTeX XML Cite \textit{C. T. Chong} et al., Adv. Math. 369, Article ID 107180, 38 p. (2020; Zbl 1444.03012) Full Text: DOI OpenURL
Willard, Dan E. On the tender line separating generalizations and boundary-case exceptions for the second incompleteness theorem under semantic tableaux deduction. (English) Zbl 07197418 Artemov, Sergei (ed.) et al., Logical foundations of computer science. International symposium, LFCS 2020, Deerfield Beach, FL, USA, January 04–07, 2020. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 11972, 268-286 (2020). MSC: 03F40 03F30 PDF BibTeX XML Cite \textit{D. E. Willard}, Lect. Notes Comput. Sci. 11972, 268--286 (2020; Zbl 07197418) Full Text: DOI OpenURL
Leivant, Daniel Finitism, imperative programs and primitive recursion. (English) Zbl 07197408 Artemov, Sergei (ed.) et al., Logical foundations of computer science. International symposium, LFCS 2020, Deerfield Beach, FL, USA, January 04–07, 2020. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 11972, 98-110 (2020). MSC: 03D20 03F30 03A05 PDF BibTeX XML Cite \textit{D. Leivant}, Lect. Notes Comput. Sci. 11972, 98--110 (2020; Zbl 07197408) Full Text: DOI OpenURL
Kushida, Hirohiko On the constructive truth and falsity in Peano arithmetic. (English) Zbl 07197406 Artemov, Sergei (ed.) et al., Logical foundations of computer science. International symposium, LFCS 2020, Deerfield Beach, FL, USA, January 04–07, 2020. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 11972, 75-84 (2020). MSC: 03F50 03F30 PDF BibTeX XML Cite \textit{H. Kushida}, Lect. Notes Comput. Sci. 11972, 75--84 (2020; Zbl 07197406) Full Text: DOI arXiv OpenURL
Hermo Reyes, Eduardo; Joosten, Joost J. The logic of Turing progressions. (English) Zbl 1452.03132 Notre Dame J. Formal Logic 61, No. 1, 155-180 (2020). Reviewer: Mladen Vuković (Zagreb) MSC: 03F45 03F30 03F03 03B45 PDF BibTeX XML Cite \textit{E. Hermo Reyes} and \textit{J. J. Joosten}, Notre Dame J. Formal Logic 61, No. 1, 155--180 (2020; Zbl 1452.03132) Full Text: DOI arXiv Euclid Link OpenURL
Sanders, Sam Splittings and disjunctions in reverse mathematics. (English) Zbl 1462.03009 Notre Dame J. Formal Logic 61, No. 1, 51-74 (2020). Reviewer: Jeffry L. Hirst (Boone) MSC: 03B30 03D65 03F35 PDF BibTeX XML Cite \textit{S. Sanders}, Notre Dame J. Formal Logic 61, No. 1, 51--74 (2020; Zbl 1462.03009) Full Text: DOI arXiv Euclid OpenURL
Freund, Anton; Pakhomov, Fedor Short proofs for slow consistency. (English) Zbl 1455.03078 Notre Dame J. Formal Logic 61, No. 1, 31-49 (2020). Reviewer: Leszek Aleksander Kołodziejczyk (Warszawa) MSC: 03F30 03F20 03F15 03F40 03D20 PDF BibTeX XML Cite \textit{A. Freund} and \textit{F. Pakhomov}, Notre Dame J. Formal Logic 61, No. 1, 31--49 (2020; Zbl 1455.03078) Full Text: DOI arXiv Euclid OpenURL
Visser, Albert Another look at the second incompleteness theorem. (English) Zbl 1444.03168 Rev. Symb. Log. 13, No. 2, 269-295 (2020). Reviewer: Victor V. Pambuccian (Glendale) MSC: 03F40 03B25 03F25 03F30 03F45 03A05 PDF BibTeX XML Cite \textit{A. Visser}, Rev. Symb. Log. 13, No. 2, 269--295 (2020; Zbl 1444.03168) Full Text: DOI OpenURL
Freund, Anton Predicative collapsing principles. (English) Zbl 1479.03007 J. Symb. Log. 85, No. 1, 511-530 (2020). Reviewer: Paul Shafer (Leeds) MSC: 03B30 03F15 03F35 PDF BibTeX XML Cite \textit{A. Freund}, J. Symb. Log. 85, No. 1, 511--530 (2020; Zbl 1479.03007) Full Text: DOI arXiv OpenURL
Enayat, Ali; Łełyk, Mateusz; Wcisło, Bartosz Truth and feasible reducibility. (English) Zbl 1444.03164 J. Symb. Log. 85, No. 1, 367-421 (2020). Reviewer: Victor V. Pambuccian (Glendale) MSC: 03F30 03C62 03D15 03H15 PDF BibTeX XML Cite \textit{A. Enayat} et al., J. Symb. Log. 85, No. 1, 367--421 (2020; Zbl 1444.03164) Full Text: DOI arXiv OpenURL
Nies, André; Shafer, Paul Randomness notions and reverse mathematics. (English) Zbl 1444.03013 J. Symb. Log. 85, No. 1, 271-299 (2020). Reviewer: Jeffry L. Hirst (Boone) MSC: 03B30 03D32 03F35 68Q30 PDF BibTeX XML Cite \textit{A. Nies} and \textit{P. Shafer}, J. Symb. Log. 85, No. 1, 271--299 (2020; Zbl 1444.03013) Full Text: DOI arXiv Link OpenURL
Astor, Eric P.; Dzhafarov, Damir; Montalbán, Antonio; Solomon, Reed; Westrick, Linda Brown The determined property of Baire in reverse math. (English) Zbl 07190471 J. Symb. Log. 85, No. 1, 166-198 (2020). MSC: 03F35 PDF BibTeX XML Cite \textit{E. P. Astor} et al., J. Symb. Log. 85, No. 1, 166--198 (2020; Zbl 07190471) Full Text: DOI arXiv OpenURL
Goris, Evan; Joosten, Joost J. Two new series of principles in the interpretability logic of all reasonable arithmetical theories. (English) Zbl 1471.03085 J. Symb. Log. 85, No. 1, 1-25 (2020). Reviewer: Osamu Sonobe (Follonica) MSC: 03F45 03F25 03B45 03B60 03F30 03F40 PDF BibTeX XML Cite \textit{E. Goris} and \textit{J. J. Joosten}, J. Symb. Log. 85, No. 1, 1--25 (2020; Zbl 1471.03085) Full Text: DOI Link OpenURL
Afshari, Bahareh; Hetzl, Stefan; Leigh, Graham E. Herbrand’s theorem as higher order recursion. (English) Zbl 1464.03085 Ann. Pure Appl. Logic 171, No. 6, Article ID 102792, 45 p. (2020). Reviewer: Annika Kanckos (Helsinki) MSC: 03F05 03F07 03D05 03F30 PDF BibTeX XML Cite \textit{B. Afshari} et al., Ann. Pure Appl. Logic 171, No. 6, Article ID 102792, 45 p. (2020; Zbl 1464.03085) Full Text: DOI OpenURL
Goh, Jun Le Embeddings between well-orderings: computability-theoretic reductions. (English) Zbl 1479.03008 Ann. Pure Appl. Logic 171, No. 6, Article ID 102789, 17 p. (2020). Reviewer: Paul Shafer (Leeds) MSC: 03B30 03D30 03D80 03F35 03D55 PDF BibTeX XML Cite \textit{J. Le Goh}, Ann. Pure Appl. Logic 171, No. 6, Article ID 102789, 17 p. (2020; Zbl 1479.03008) Full Text: DOI OpenURL
Walsh, James A note on the consistency operator. (English) Zbl 1443.03042 Proc. Am. Math. Soc. 148, No. 6, 2645-2654 (2020). Reviewer: Anton Freund (Darmstadt) MSC: 03F40 03F25 03F35 PDF BibTeX XML Cite \textit{J. Walsh}, Proc. Am. Math. Soc. 148, No. 6, 2645--2654 (2020; Zbl 1443.03042) Full Text: DOI arXiv OpenURL
Powell, Thomas Dependent choice as a termination principle. (English) Zbl 1481.03040 Arch. Math. Logic 59, No. 3-4, 503-516 (2020). MSC: 03D65 03F35 03B30 68Q42 PDF BibTeX XML Cite \textit{T. Powell}, Arch. Math. Logic 59, No. 3--4, 503--516 (2020; Zbl 1481.03040) Full Text: DOI arXiv OpenURL
Jeřábek, Emil Induction rules in bounded arithmetic. (English) Zbl 1471.03082 Arch. Math. Logic 59, No. 3-4, 461-501 (2020). Reviewer: Ariel Germán Fernández (Buenos Aires) MSC: 03F30 03F20 PDF BibTeX XML Cite \textit{E. Jeřábek}, Arch. Math. Logic 59, No. 3--4, 461--501 (2020; Zbl 1471.03082) Full Text: DOI arXiv OpenURL
Arai, Toshiyasu Proof-theoretic strengths of the well-ordering principles. (English) Zbl 1481.03063 Arch. Math. Logic 59, No. 3-4, 257-275 (2020). MSC: 03F15 03F35 03B30 PDF BibTeX XML Cite \textit{T. Arai}, Arch. Math. Logic 59, No. 3--4, 257--275 (2020; Zbl 1481.03063) Full Text: DOI arXiv OpenURL
Normann, Dag; Sanders, Sam Pincherle’s theorem in reverse mathematics and computability theory. (English) Zbl 1443.03008 Ann. Pure Appl. Logic 171, No. 5, Article ID 102788, 41 p. (2020). Reviewer: Jeffry L. Hirst (Boone) MSC: 03B30 03D65 03F35 03D80 PDF BibTeX XML Cite \textit{D. Normann} and \textit{S. Sanders}, Ann. Pure Appl. Logic 171, No. 5, Article ID 102788, 41 p. (2020; Zbl 1443.03008) Full Text: DOI arXiv OpenURL
Cholak, Peter; Patey, Ludovic Thin set theorems and cone avoidance. (English) Zbl 1442.03007 Trans. Am. Math. Soc. 373, No. 4, 2743-2773 (2020). Reviewer: Jeffry L. Hirst (Boone) MSC: 03B30 03F35 03D80 05D10 PDF BibTeX XML Cite \textit{P. Cholak} and \textit{L. Patey}, Trans. Am. Math. Soc. 373, No. 4, 2743--2773 (2020; Zbl 1442.03007) Full Text: DOI arXiv OpenURL
Bydžovský, Jan; Müller, Moritz Polynomial time ultrapowers and the consistency of circuit lower bounds. (English) Zbl 1480.03016 Arch. Math. Logic 59, No. 1-2, 127-147 (2020). MSC: 03C20 03F30 03C98 03C62 68Q17 PDF BibTeX XML Cite \textit{J. Bydžovský} and \textit{M. Müller}, Arch. Math. Logic 59, No. 1--2, 127--147 (2020; Zbl 1480.03016) Full Text: DOI Link OpenURL
Sato, Kentaro Elementary inductive dichotomy: separation of open and clopen determinacies with infinite alternatives. (English) Zbl 1476.03075 Ann. Pure Appl. Logic 171, No. 3, Article ID 102754, 64 p. (2020). Reviewer: Reinhard Kahle (Lisboa) MSC: 03E70 03F35 03D70 03E60 03B30 PDF BibTeX XML Cite \textit{K. Sato}, Ann. Pure Appl. Logic 171, No. 3, Article ID 102754, 64 p. (2020; Zbl 1476.03075) Full Text: DOI OpenURL
Dutilh Novaes, Catarina Axiomatizations of arithmetic and the first-order/second-order divide. (English) Zbl 1475.03089 Synthese 196, No. 7, 2583-2597 (2019). MSC: 03C62 03F30 03F35 03A05 PDF BibTeX XML Cite \textit{C. Dutilh Novaes}, Synthese 196, No. 7, 2583--2597 (2019; Zbl 1475.03089) Full Text: DOI OpenURL
Fujimoto, Kentaro Deflationism beyond arithmetic. (English) Zbl 1474.03019 Synthese 196, No. 3, 1045-1069 (2019). MSC: 03A05 03F30 03F35 PDF BibTeX XML Cite \textit{K. Fujimoto}, Synthese 196, No. 3, 1045--1069 (2019; Zbl 1474.03019) Full Text: DOI OpenURL
Nicolai, Carlo; Piazza, Mario The implicit commitment of arithmetical theories and its semantic core. (English) Zbl 1474.03033 Erkenntnis 84, No. 4, 913-937 (2019). MSC: 03A05 03F30 PDF BibTeX XML Cite \textit{C. Nicolai} and \textit{M. Piazza}, Erkenntnis 84, No. 4, 913--937 (2019; Zbl 1474.03033) Full Text: DOI OpenURL
von Plato, Jan What are the axioms for numbers and who invented them? (English) Zbl 1465.03042 Mras, Gabriele M. (ed.) et al., Philosophy of logic and mathematics. Proceedings of the 41st international Ludwig Wittgenstein symposium. Berlin: De Gruyter. Publ. Austrian Ludwig Wittgenstein Soc. New Ser. 27, 343-356 (2019). MSC: 03A05 00A30 03F30 PDF BibTeX XML Cite \textit{J. von Plato}, Publ. Austrian Ludwig Wittgenstein Soc. New Ser. 27, 343--356 (2019; Zbl 1465.03042) Full Text: DOI OpenURL
Parsons, Charles Remarks on two papers of Paul Bernays. (English) Zbl 1465.03033 Mras, Gabriele M. (ed.) et al., Philosophy of logic and mathematics. Proceedings of the 41st international Ludwig Wittgenstein symposium. Berlin: De Gruyter. Publ. Austrian Ludwig Wittgenstein Soc. New Ser. 27, 297-312 (2019). MSC: 03A05 00A30 03F25 03F30 03-03 01A60 PDF BibTeX XML Cite \textit{C. Parsons}, Publ. Austrian Ludwig Wittgenstein Soc. New Ser. 27, 297--312 (2019; Zbl 1465.03033) Full Text: DOI OpenURL
Tait, William What Hilbert and Bernays meant by “finitism”. (English) Zbl 1465.03040 Mras, Gabriele M. (ed.) et al., Philosophy of logic and mathematics. Proceedings of the 41st international Ludwig Wittgenstein symposium. Berlin: De Gruyter. Publ. Austrian Ludwig Wittgenstein Soc. New Ser. 27, 249-261 (2019). MSC: 03A05 03-03 00A30 03F30 PDF BibTeX XML Cite \textit{W. Tait}, Publ. Austrian Ludwig Wittgenstein Soc. New Ser. 27, 249--261 (2019; Zbl 1465.03040) Full Text: DOI OpenURL
Kremer, Michael Definitions in Begriffsschrift and Grundgesetze. (English) Zbl 1465.03015 Ebert, Philip A. (ed.) et al., Essays on Frege’s Basic laws of arithmetic. Oxford: Oxford University Press. 538-566 (2019). MSC: 03-03 03A05 01A55 01A60 03F30 PDF BibTeX XML Cite \textit{M. Kremer}, in: Essays on Frege's \textit {Basic laws of arithmetic}. Oxford: Oxford University Press. 538--566 (2019; Zbl 1465.03015) Full Text: DOI OpenURL