×

In memoriam: James Earl Baumgartner (1943–2011). (English) Zbl 1402.03012

Summary: James Earl Baumgartner (March 23, 1943–December 28, 2011) came of age mathematically during the emergence of forcing as a fundamental technique of set theory, and his seminal research changed the way set theory is done. He made fundamental contributions to the development of forcing, to our understanding of uncountable orders, to the partition calculus, and to large cardinals and their ideals. He promulgated the use of logic such as absoluteness and elementary submodels to solve problems in set theory, he applied his knowledge of set theory to a variety of areas in collaboration with other mathematicians, and he encouraged a community of mathematicians with engaging survey talks, enthusiastic discussions of open problems, and friendly mathematical conversations.

MSC:

03-03 History of mathematical logic and foundations
01A70 Biographies, obituaries, personalia, bibliographies
03E35 Consistency and independence results

Biographic References:

Baumgartner, James Earl
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Abraham, U., Rubin, M., Shelah, S.: On the consistency of some partition theorems for continuous colorings, and the structure of \[\aleph_1\] ℵ1-dense real order types. Ann. Pure Appl. Log. 29(2), 123-206 (1985) · Zbl 0585.03019
[2] Abraham, U., Shelah, S.: Forcing closed unbounded sets. J. Symb. Log. 48(3), 643-657 (1983) · Zbl 0568.03024
[3] Bagaria, J.: Book Review: Large cardinals imply that every reasonably definable set of reals is Lebesgue measurable by Saharon Shelah and Hugh Woodin. Bull. Symb. Log. 8(8), 543-545 (2002)
[4] Balcerzak, M., Hejduk, J., Baumgartner, J.E.: On certain \[\sigma\] σ-ideals of sets. Real Anal. Exch. 14(2), 447-453 (1988/89) · Zbl 0679.28002
[5] Banach, S.: Uber additive massfunktionen in alstrakten mengen. Fund. Math. 15, 97-101 (1930) · JFM 56.0920.03
[6] Baumgartner, J.E.: On the cardinality of dense subsets of linear orderings I. Not. Am. Math. Soc. 15, 935 (1968). Abstract, preliminary report · Zbl 0742.03017
[7] Baumgartner, J.E.: Undefinability of \[n\] n-ary relations from unary functions. Not. Am. Math. Soc. 17, 842-843 (1969). Abstract, preliminary report · Zbl 0532.03023
[8] Baumgartner, J.E.: Decompositions and embeddings of trees. Not. Am. Math. Soc. 18, 967 (1970). Abstract, preliminary report · JFM 54.0092.01
[9] Baumgartner, J.E.: Results and Independence Proofs in Combinatorial Set Theory. PhD thesis, University of California, Berkeley (1970) · Zbl 0451.03017
[10] Baumgartner, J.E.: A possible extension of Cantor’s theorem on the rationals. Not. Am. Math. Soc. 18, 428-429 (1971). Abstract, preliminary report · Zbl 1345.03092
[11] Baumgartner, J.E.: All \[\aleph_1\] ℵ1-dense sets of reals can be isomorphic. Fund. Math. 79(2), 101-106 (1973) · Zbl 0274.02037
[12] Baumgartner, J.E.: The Hanf number for complete \[{L}_{\omega_1,\omega }\] Lω1,ω-sentences (without GCH). J. Symb. Log. 39, 575-578 (1974) · Zbl 0299.02063
[13] Baumgartner, J.E.: Improvement of a partition theorem of Erdős and Rado. J. Comb. Theory Ser. A 17, 134-137 (1974) · Zbl 0282.05003
[14] Baumgartner, J.E.: A short proof of Hindman’s theorem. J. Comb. Theory Ser. A 17, 384-386 (1974) · Zbl 0289.05009
[15] Baumgartner, J.E.: Some results in the partition calculus. Not. Am. Math. Soc. 21, A-29 (1974). Abstract, preliminary report · Zbl 1251.03059
[16] Baumgartner, J.E.: Canonical partition relations. J. Symb. Log. 40(4), 541-554 (1975) · Zbl 0325.04006
[17] Baumgartner, J.E.: Ineffability properties of cardinals. I. In: Infinite and Finite Sets (Colloq., Keszthely, 1973; dedicated to P. Erdős on his 60th birthday), Vol. I, volume 10 of Colloq. Math. Soc. János Bolyai, pp. 109-130. North-Holland, Amsterdam (1975) · Zbl 1153.03315
[18] Baumgartner, J.E.: Partition relations for uncountable ordinals. Isr. J. Math. 21(4), 296-307 (1975) · Zbl 0323.02066
[19] Baumgartner, J.E.: Partitioning vector spaces. J. Comb. Theory Ser. A 18, 231-233 (1975) · Zbl 0298.05005
[20] Baumgartner, J.E.: Topological properties of Specker types. Not. Am. Math. Soc. 22, A-219 (1975). Abstract, preliminary report
[21] Baumgartner, J.E.: Almost-disjoint sets, the dense set problem and the partition calculus. Ann. Math. Log. 9(4), 401-439 (1976) · Zbl 0339.04003
[22] Baumgartner, J.E.: A new class of order types. Ann. Math. Log. 9(3), 187-222 (1976) · Zbl 0339.04002
[23] Baumgartner, J.E.: Ineffability properties of cardinals. II. In: Logic, foundations of mathematics and computability theory (Proc. Fifth Internat. Congr. Logic, Methodology and Philos. of Sci., Univ. Western Ontario, London, Ont., 1975), Part I, pp. 87-106. Univ. Western Ontario Ser. Philos. Sci., Vol. 9. Reidel, Dordrecht (1977) · Zbl 0313.04002
[24] Baumgartner, J.E.: Independence results in set theory. Not. Am. Math. Soc. 25, A248-249 (1978)
[25] Baumgartner, J.E.: Independence proofs and combinatorics. In: Relations Between Combinatorics and Other Parts of Mathematics (Proc. Sympos. Pure Math., Ohio State Univ., Columbus, Ohio, 1978), Proc. Sympos. Pure Math., XXXIV, pp. 35-46. Am. Math. Soc., Providence, R.I. (1979) · Zbl 0357.28003
[26] Baumgartner, J.E.: Chains and antichains in \[{\cal{P}}(\omega )P\](ω). J. Symb. Log. 45(1), 85-92 (1980) · Zbl 0437.03027
[27] Baumgartner, J.E.: Order types of real numbers and other uncountable orderings. In: Ordered Sets (Banff, Alta., 1981), volume 83 of NATO Adv. Study Inst. Ser. C: Math. Phys. Sci., pp. 239-277. Reidel, Dordrecht (1982) · Zbl 0945.03076
[28] Baumgartner, J.E.: Iterated forcing. In: Surveys in Set Theory, volume 87 of London Math. Soc. Lecture Note Ser., pp. 1-59. Cambridge Univ. Press, Cambridge (1983) · Zbl 0524.03040
[29] Baumgartner, J.E.: Applications of the proper forcing axiom. In: Handbook of Set-Theoretic Topology, pp. 913-959. North-Holland, Amsterdam (1984) · Zbl 0381.03039
[30] Baumgartner, J.E.: Generic graph construction. J. Symb. Log. 49(1), 234-240 (1984) · Zbl 0573.03021
[31] Baumgartner, J.E.: Bases for Aronszajn trees. Tsukuba J. Math. 9(1), 31-40 (1985) · Zbl 0574.03036
[32] Baumgartner, J.E.: Sacks forcing and the total failure of Martin’s Axiom. Topol. Appl. 19(3), 211-225 (1985) · Zbl 0579.03038
[33] Baumgartner, J.E.: Book Review: Set theory. An introduction to independence proofs by Kenneth Kunen. J. Symb. Log. 51(2), 462-464 (1986)
[34] Baumgartner, JE, Polarized partition relations and almost-disjoint functions, 213-222 (1989), Amsterdam
[35] Baumgartner, J.E.: Remarks on partition ordinals. In: Set Theory and Its Applications (Toronto, ON, 1987), volume 1401 of Lecture Notes in Math., pp. 5-17. Springer, Berlin (1989) · JFM 64.0037.02
[36] Baumgartner, J.E.: Is there a different proof of the Erdős-Rado theorem? In A tribute to Paul Erdős, pp. 27-37. Cambridge Univ. Press, Cambridge (1990) · Zbl 0744.03047
[37] Baumgartner, J.E.: On the size of closed unbounded sets. Ann. Pure Appl. Log. 54(3), 195-227 (1991) · Zbl 0746.03040
[38] Baumgartner, J.E.: The future of modern set theory. Ann. Jpn. Assoc. Philos. Sci. 8(4), 187-190 (1994) · Zbl 0819.03041
[39] Baumgartner, J.E.: Ultrafilters on \[\omega\] ω. J. Symb. Log. 60(2), 624-639 (1995) · Zbl 0834.04005
[40] Baumgartner, J.E.: In Memoriam: Paul Erdős 1913-1996. Bull. Symb. Log. 3(1), 70-71 (1997) · Zbl 0876.01046
[41] Baumgartner, J.E.: Hajnal’s contributions to combinatorial set theory and the partition calculus. In: Set Theory (Piscataway, NJ, 1999), volume 58 of DIMACS Ser. Discrete Math. Theoret. Comput. Sci., pp. 25-30. Am. Math. Soc., Providence, RI (2002) · Zbl 1016.03045
[42] Baumgartner, J.E., Dordal, P.: Adjoining dominating functions. J. Symb. Log. 50(1), 94-101 (1985) · Zbl 0566.03031
[43] Baumgartner, J.E., Erdős, P., Higgs, D.A.: Cross-cuts in the power set of an infinite set. Order 1(2), 139-145 (1984) · Zbl 0559.04009
[44] Baumgartner, J.E., Frankiewicz, R., Zbierski, P.: Embedding of Boolean algebras in \[P(\omega )/{\text{ fin }}P\](ω)/fin. Fund. Math. 136(3), 187-192 (1990) · Zbl 0718.03039
[45] Baumgartner, J.E., Galvin, F.: Generalized Erdős cardinals and \[0^{\#}0\]#. Ann. Math. Log. 15(3), 289-313 (1979), 1978 · Zbl 0437.03028
[46] Baumgartner, J.E., Galvin, F., Laver, R., McKenzie, R.: Game theoretic versions of partition relations. In: Infinite and Finite Sets (Colloq., Keszthely, 1973; dedicated to P. Erdős on his 60th birthday), Vol. I, volume 10 of Colloq. Math. Soc. János Bolyai, pp. 131-135. North-Holland, Amsterdam (1975) · Zbl 0307.90097
[47] Baumgartner, J.E., Hajnal, A.: A proof (involving Martin’s Axiom) of a partition relation. Yellow Series of the University of Calgary, Research Paper 122, April 1971. Fund. Math. 78(3), 193-203 (1973) · Zbl 0257.02054
[48] Baumgartner, J.E., Hajnal, A.: A remark on partition relations for infinite ordinals with an application to finite combinatorics. In: Logic and Combinatorics (Arcata, Calif., 1985), volume 65 of Contemp. Math., pp. 157-167. Am. Math. Soc., Providence, RI (1987) · Zbl 1109.03043
[49] Baumgartner, J.E., Hajnal, A.: Polarized partition relations. J. Symb. Log. 66(2), 811-821 (2001) · Zbl 0994.03036
[50] Baumgartner, J.E., Hajnal, A., Máté, A.: Weak saturation properties of ideals. In: Infinite and Finite Sets (Colloq., Keszthely, 1973; dedicated to P. Erdős on his 60th birthday), Vol. I, volume 10 of Colloq. Math. Soc. János Bolyai, pp. 137-158. North-Holland, Amsterdam (1975) · Zbl 0316.02072
[51] Baumgartner, JE; Hajnal, A.; Todorcevic, S., Extensions of the Erdős-Rado theorem, 1-17 (1993), Dordrecht · Zbl 0846.03021
[52] Baumgartner, J.E., Harrington, L., Kleinberg, E.: Adding a closed unbounded set. J. Symb. Log. 41, 481-482 (1976) · Zbl 0344.02044
[53] Baumgartner, J.E., Komjáth, P.: Boolean algebras in which every chain and antichain is countable. Fund. Math. 111(2), 125-133 (1981) · Zbl 0452.03044
[54] Baumgartner, J.E., Larson, J.A.: A diamond example of an ordinal graph with no infinite paths. Ann. Pure Appl. Log. 47(1), 1-10 (1990) · Zbl 0703.03028
[55] Baumgartner, J.E., Laver, R.: Iterated perfect-set forcing. Ann. Math. Log. 17(3), 271-288 (1979) · Zbl 0427.03043
[56] Baumgartner, J.E., Martin, D.A., Shelah, S. (eds.): Axiomatic set theory, volume 31 of Contemporary Mathematics, Providence, RI (1984). American Mathematical Society · Zbl 1079.03039
[57] Baumgartner, J.E., Prikry, K.: On a theorem of Silver. Discrete Math. 14(1), 17-21 (1976) · Zbl 0325.04007
[58] Baumgartner, J.E., Prikry, K.: Singular cardinals and the generalized continuum hypothesis. Am. Math. Mon. 84(2), 108-113 (1977) · Zbl 0362.02075
[59] Baumgartner, J.E., Shelah, S.: Remarks on superatomic Boolean algebras. Ann. Pure Appl. Log. 33(2), 109-129 (1987) · Zbl 0643.03038
[60] Baumgartner, J.E., Shelah, S., Thomas, S.: Maximal subgroups of infinite symmetric groups. Notre Dame J. Formal Log. 34(1), 1-11 (1993) · Zbl 0788.03067
[61] Baumgartner, J.E., Spinas, O.: Independence and consistency proofs in quadratic form theory. J. Symb. Log. 56(4), 1195-1211 (1991) · Zbl 0745.03040
[62] Baumgartner, J.E., Tall, F.D.: Reflecting Lindelöfness. In: Proceedings of the International Conference on Topology and its Applications (Yokohama, 1999), vol. 122, pp. 35-49 (2002) · Zbl 1006.54031
[63] Baumgartner, J.E., Taylor, A.D.: Partition theorems and ultrafilters. Trans. Am. Math. Soc. 241, 283-309 (1978) · Zbl 0386.03024
[64] Baumgartner, J.E., Taylor, A.D.: Saturation properties of ideals in generic extensions. I. Trans. Am. Math. Soc. 270(2), 557-574 (1982) · Zbl 0485.03022
[65] Baumgartner, J.E., Taylor, A.D.: Saturation properties of ideals in generic extensions. II. Trans. Am. Math. Soc. 271(2), 587-609 (1982) · Zbl 0496.03029
[66] Baumgartner, J.E., Taylor, A.D., Wagon, S.: On splitting stationary subsets of large cardinals. J. Symb. Log. 42(2), 203-214 (1977) · Zbl 0373.02047
[67] Baumgartner, J.E., Taylor, A.D., Wagon, S.: Ideals on uncountable cardinals. In: Logic Colloquium ’77 (Proc. Conf., Wrocław, 1977), volume 96 of Stud. Logic Foundations Math., pp. 67-77. North-Holland, Amsterdam (1978) · Zbl 0452.03038
[68] Baumgartner, J.E., van Douwen, E.K.: Strong realcompactness and weakly measurable cardinals. Topol. Appl. 35(2-3), 239-251 (1990) · Zbl 0698.54019
[69] Baumgartner, J.E., Weese, M.: Partition algebras for almost-disjoint families. Trans. Am. Math. Soc. 274(2), 619-630 (1982) · Zbl 0515.03032
[70] Beller, A., Litman, A.: A strengthening of Jensen’s \[cm\] cm principles. J. Symb. Log. 45(2), 251-264 (1980) · Zbl 0457.03049
[71] Brech, C., Koszmider, P.: On universal Banach spaces of density continuum. Isr. J. Math. 190, 93-110 (2012) · Zbl 1271.46019
[72] Brodsky, A.M.: A theory of stationary trees and the balanced Baumgartner-Hajnal-Todorcevic theorem for trees. Acta Math. Hungar. 144(2), 285-352 (2014) · Zbl 1324.03013
[73] Chang, C.C., Keisler, H.J.: Model Theory. North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York (1973). Studies in Logic and the Foundations of Mathematics, vol. 73 · Zbl 0276.02032
[74] Claverie, B., Schindler, R.: Woodin’s axiom \[(\ast )(*)\], bounded forcing axioms, and precipitous ideals on \[\omega_1\] ω1. J. Symb. Log. 77(2), 475-498 (2012) · Zbl 1250.03111
[75] Cummings, J.: Iterated forcing and elementary embeddings. In: Handbook of Set Theory, pp. 775-883. Springer, Dordrecht (2010) · Zbl 1198.03060
[76] Devlin, K.J.: The Yorkshireman’s guide to proper forcing. In: Surveys in Set Theory, volume 87 of London Math. Soc. Lecture Note Ser., pp. 60-115. Cambridge Univ. Press, Cambridge (1983) · Zbl 0524.03041
[77] Devlin, K.J., Johnsbråten, H.: The Souslin Problem. Lecture Notes in Mathematics, vol. 405. Springer, Berlin (1974) · Zbl 0289.02043
[78] Easton, W.B.: Powers of Regular Cardinals. PhD thesis, Princeton University, Princeton, NJ (1964). Advisor A. Church · Zbl 0209.30601
[79] Erdős, P.: Some set-theoretical properties of graphs. Rev. Univ. Nac. Tucumán Ser. A 3, 363-367 (1942) · Zbl 0063.01265
[80] Erdős, P., Hajnal, A.: Solved and unsolved problems in set theory. In: Proceedings of the Tarski Symposium (Proc. Sympos. Pure Math., UC Berkeley, CA, 1971), vol. 25, pp 261-265. Am. Math. Soc., Providence, R.I. (1974) · Zbl 0285.04002
[81] Erdős, P., Hajnal, A.: Unsolved problems in set theory. In: Axiomatic Set Theory (Proc. Sympos. Pure Math., UCLA, 1967), vol. 13, pp. 17-48. Am. Math. Soc., Providence, R.I. (1971) · Zbl 0228.04001
[82] Erdős, P., Hajnal, A., Rado, R.: Partition relations for cardinal numbers. Acta Math. Acad. Sci. Hungar. 16, 93-196 (1965) · Zbl 0158.26603
[83] Erdős, P., Rado, R.: A problem on ordered sets. J. Lond. Math. Soc. (2) 28(4), 426-438 (1953) · Zbl 0051.04003
[84] Erdős, P., Rado, R.: A partition calculus in set theory. Bull. Am. Math. Soc. 62, 427-489 (1956) · Zbl 0071.05105
[85] Erdős, P., Tarski, A.: On families of mutually exclusive sets. Ann. Math. (2) 44(2), 315-329 (1943) · Zbl 0060.12602
[86] Erdős, P.: Problems and results on finite and infinite combinatorial analysis. In: Infinite and finite sets (Colloq., Keszthely, 1973; dedicated to P. Erdős on his 60th birthday), Vol. I, pp. 403-424. Colloq. Math. Soc. János Bolyai, Vol. 10. North-Holland, Amsterdam (1975) · Zbl 0643.03038
[87] Erdős, P., Hajnal, A.: On a property of families of sets. Acta Math. Acad. Sci. Hungar. 12, 87-123 (1961) · Zbl 0201.32801
[88] Erdős, P., Hajnal, A.: Some remarks concerning our paper “On the structure of set-mappings”. Non-existence of a two-valued \[\sigma\] σ-measure for the first uncountable inaccessible cardinal. Acta Math. Acad. Sci. Hungar. 13, 223-226 (1962) · Zbl 0134.01602
[89] Erdős, P., Hajnal, A.: On chromatic number of graphs and set-systems. Acta Math. Acad. Sci. Hungar. 17, 61-99 (1966) · Zbl 0151.33701
[90] Erdös, P., Rado, R.: A partition calculus in set theory. Bull. Am. Math. Soc. 62, 427-489 (1956) · Zbl 0071.05105
[91] Erdős, P., Tarski, A.: On some problems involving inaccessible cardinals. In: Essays on the Foundations of Mathematics, pp. 50-82. Magnes Press, Hebrew Univ., Jerusalem (1961) · Zbl 0212.32502
[92] Eskew, M.: Measurability Properties on Small Cardinals. PhD thesis, University of California, Irvine, CA (2014). Advisor M. Zeman · Zbl 0579.03038
[93] Feng, Q.: A hierarchy of Ramsey cardinals. Ann. Pure Appl. Log. 49(3), 257-277 (1990) · Zbl 0719.03025
[94] Fleissner, W.G., Kunen, K.: Barely Baire spaces. Fund. Math. 101(3), 229-240 (1978) · Zbl 0413.54036
[95] Foreman, M.: Chang’s conjecture, generic elementary embeddings and inner models for huge cardinals. Bull. Symb. Log. 21(3), 251-269 (2015) · Zbl 1371.03054
[96] Foreman, M., Hajnal, A.: A partition relation for successors of large cardinals. Math. Ann. 325(3), 583-623 (2003) · Zbl 1024.03050
[97] Foreman, M., Laver, R.: Some downwards transfer properties for \[\aleph_2\] ℵ2. Adv. Math. 67(2), 230-238 (1988) · Zbl 0659.03033
[98] Foreman, M., Magidor, M.: Large cardinals and definable counterexamples to the continuum hypothesis. Ann. Pure Appl. Log. 76(1), 47-97 (1995) · Zbl 0837.03040
[99] Foreman, M., Magidor, M., Shelah, S.: Martin’s maximum, saturated ideals and nonregular ultrafilters. II. Ann. Math. (2) 127(3), 521-545 (1988) · Zbl 0645.03028
[100] Friedman, H.M.: On closed sets of ordinals. Proc. Am. Math. Soc. 43, 190-192 (1974) · Zbl 0299.04003
[101] Friedman, H.M.: Subtle cardinals and linear orderings. Ann. Pure Appl. Log. 107(1-3), 1-34 (2001) · Zbl 0966.03048
[102] Friedman, S.-D.: Forcing with finite conditions. In: Set theory, Trends Math., pp. 285-295. Birkhäuser, Basel (2006) · Zbl 1113.03045
[103] Gaifman, H., Specker, E.: Isomorphism types of trees. Proc. Am. Math. Soc. 15, 1-7 (1964) · Zbl 0125.01203
[104] Galvin, F.: Chromatic numbers of subgraphs. Period. Math. Hungar. 4, 117-119 (1973) · Zbl 0278.05105
[105] Galvin, F.: On a partition theorem of Baumgartner and Hajnal. In: Infinite and Finite Sets (Colloq., Keszthely, 1973; dedicated to P. Erdős on his 60th birthday), Vol. II, pp. 711-729. Colloq. Math. Soc. János Bolyai, Vol. 10. North-Holland, Amsterdam (1975) · Zbl 0559.04009
[106] Gitik, M.: On normal precipitous ideals. Isr. J. Math. 175, 191-219 (2010) · Zbl 1200.03030
[107] Gitik, M., Shelah, S.: Less saturated ideals. Proc. Am. Math. Soc. 125(5), 1523-1530 (1997) · Zbl 0864.03031
[108] Hajnal, A.: Private conversation on Baumgartner-Hajnal Theorem. Jean Larson interviewed Hajnal at the Erdős Centennial in Budapest, July 2013 · Zbl 1367.03094
[109] Halbeisen, L.: Families of almost disjoint Hamel bases. Extr. Math. 20(2), 199-202 (2005) · Zbl 1099.46013
[110] Harrington, L., Shelah, S.: Some exact equiconsistency results in set theory. Notre Dame J. Formal Log. 26(2), 178-188 (1985) · Zbl 0579.03039
[111] Hausdorff, F.: Untersuchungen über Ordnugstypen IV, V. Berichte über die Verlhandlungen der Königlich Säsischen Gesellschaft der Wissenschaften zu Leipzig, Mathematisch-Physiche Klasse 59, 84-159 (1907) · Zbl 0746.03040
[112] Hausdorff, F.: Grundzüge einer Theorie der geordnete Mengenlehre. Math. Ann. 65, 435-505 (1908) · JFM 39.0099.01
[113] Ishiu, T.: \[ \alpha\] α-properness and Axiom A. Fund. Math. 186(1), 25-37 (2005) · Zbl 1079.03039
[114] Jech, T.: Non-provability of Souslin’s hypothesis. Comment. Math. Univ. Carol. 8(2), 291-305 (1967) · Zbl 0204.00701
[115] Jech, T.: Set Theory. Springer Monographs in Mathematics. Springer, Berlin (2003). The third millennium edition, revised and expanded · JFM 54.0092.01
[116] Jech, T., Prikry, K.: On ideals of sets and the power set operation. Bull. Am. Math. Soc. 82(4), 593-595 (1976) · Zbl 0339.02060
[117] Jech, T. (ed.): Axiomatic set theory. Proc. Sympos. Pure Math., Vol. XIII, Part II, Univ. California, Los Angeles, Calif., 1967. American Mathematical Society, Providence, R.I. (1974) · JFM 56.0920.04
[118] Jensen, R.B.: Modelle der Mengenlehre. Widerspruchsfreiheit und Unabhängigkeit der Kontinuum-Hypothese und des Auswahlaxioms. Ausgearbeitet von Franz Josef Leven. Lecture Notes in Mathematics, No. 37. Springer, Berlin (1967) · Zbl 0191.29901
[119] Jensen, R.B.: The fine structure of the constructible hierarchy. Ann. Math. Log. 4, 229-308; erratum, ibid. 4 (1972), 443, 1972. With a section by Jack Silver · Zbl 0257.02035
[120] Jensen, R.B., Kunen, K.: Some Combinatorial Properties of \[L\] L and \[VV\]. Handwritten manuscript, scanned and posted to the Jensen website, April 1969 · Zbl 0339.04003
[121] Jensen, R.B., Schimmerling, E., Schindler, R., Steel, J.R.: Stacking mice. J. Symb. Log. 74(1), 315-335 (2009) · Zbl 1161.03031
[122] Jensen, R.B., Steel, J.R.: \[KK\] without the measurable. J. Symb. Log. 78(3), 708-734 (2013) · Zbl 1348.03049
[123] Jones, A.L.: A polarized partition relation for weakly compact cardinals using elementary substructures. J. Symb. Log. 71(4), 1342-1352 (2006) · Zbl 1109.03043
[124] Kanamori, A.: The higher infinite. Springer Monographs in Mathematics. Springer, Berlin, 2d edn (2009). Large cardinals in set theory from their beginnings, Paperback reprint of the 2003 edition · Zbl 1154.03033
[125] Kanamori, A., Magidor, M.: The evolution of large cardinal axioms in set theory. In: Higher Set Theory (Proc. Conf., Math. Forschungsinst., Oberwolfach, 1977), volume 669 of Lecture Notes in Math., pp. 99-275. Springer, Berlin (1978) · Zbl 0381.03038
[126] Keisler, H.J., Tarski, A.: From accessible to inaccessible cardinals. Results holding for all accessible cardinal numbers and the problem of their extension to inaccessible ones. Fund. Math. 53, 225-308 (1963/1964). Corrections on page 119 of volume 55 (1965) · Zbl 0173.00802
[127] Komjáth, P.: Consistency results on infinite graphs. Isr. J. Math. 61, 285-294 (1988) · Zbl 0668.05031
[128] Komjáth, P.: Subgraph chromatic number. In: Set theory (Piscataway, NJ, 1999), volume 58 of DIMACS Ser. Discrete Math. Theoret. Comput. Sci., pp. 99-106. Am. Math. Soc., Providence, RI (2002) · Zbl 1023.03044
[129] Krueger, J.: Fat sets and saturated ideals. J. Symb. Log. 68(3), 837-845 (2003) · Zbl 1056.03024
[130] Krueger, J.: Adding a club with finite conditions, Part II. Arch. Math. Log. 54(1-2), 161-172 (2015) · Zbl 1408.03033
[131] Krueger, J., Schimmerling, E.: An equiconsistency result on partial squares. J. Math. Log. 11(1), 29-59 (2011) · Zbl 1258.03068
[132] Kunen, K.: Some applications of iterated ultrapowers in set theory. Ann. Math. Log. 1, 179-227 (1970) · Zbl 0236.02053
[133] Kunen, K.: Saturated ideals. J. Symb. Log. 43(1), 65-76 (1978) · Zbl 0395.03031
[134] Kurepa, Đ.: Ensembles ordonnées et ramifiés. Publ. Math. Univ. Belgrade 4, 1-138 (1935). A35 · JFM 61.0980.01
[135] Kurepa, Đ.: Ensembles linéaires et une classe de tableaux ramifiés (Tableaux ramifiés de M. Aronszajn). Publ. Inst. Math. (Beograd) 6, 129-160 (1937) · Zbl 0020.10802
[136] Kurepa, Đ.: Sur la puissance des ensembles partillement ordonnés. C. R. Soc. Sci. Varsovie, Cl. Math. 32, 61-67 (1939). Sometimes the journal is listed in Polish: Sprawozdania Towarzystwo Naukowe Warszawa Mat.-Fiz. as in the Math Review by Bagemihl · Zbl 1324.03013
[137] Larson, P.: Separating stationary reflection principles. J. Symb. Log. 65(1), 247-258 (2000) · Zbl 0945.03076
[138] Laver, R.: Order Types and Well-Quasi-Orderings. PhD thesis, University of California, Berkeley (1969). Advisor R. McKenzie · Zbl 1153.03315
[139] Laver, R.: On the consistency of Borel’s conjecture. Acta Math. 137(3-4), 151-169 (1976) · Zbl 0357.28003
[140] Laver, R.: Making the supercompactness of \[\kappa\] κ indestructible under \[\kappa\] κ-directed closed forcing. Isr. J. Math. 29(4), 385-388 (1978) · Zbl 0381.03039
[141] Magidor, M.: There are many normal ultrafiltres corresponding to a supercompact cardinal. Isr. J. Math. 9, 186-192 (1971) · Zbl 0211.30902
[142] Magidor, M.: Reflecting stationary sets. J. Symb. Log. 47(4), 755-771 (1983), 1982 · Zbl 0506.03014
[143] Malitz, JI, The Hanf number for complete \[{L}_{\omega_1,\omega }\] Lω1,ω-sentences, 166-181 (1968), Berlin
[144] Martínez, J.C.: A consistency result on thin-very tall Boolean algebras. Isr. J. Math 123, 273-284 (2001) · Zbl 0980.03056
[145] Martínez, J.C.: On cardinal sequences of LCS spaces. Topol. Appl. 203, 91-97 (2016) · Zbl 1419.54004
[146] Matet, P.: Partition relations for \[\kappa\] κ-normal ideals on \[P_\kappa (\lambda )\] Pκ(λ). Ann. Pure Appl. Log. 121(1), 89-111 (2003) · Zbl 1030.03031
[147] Milner, E.C., Prikry, K.: A partition relation for triples using a model of Todorčević. Discrete Math. 95(1-3), 183-191 (1991). Directions in infinite graph theory and combinatorics (Cambridge, 1989) · Zbl 0757.03022
[148] Mitchell, W.J.: Aronszajn Trees and the Independence of the Transfer Property. PhD thesis, University of California, Berkeley (1970). Advisor J. Silver · Zbl 0255.02069
[149] Mitchell, W.J.: Aronszajn trees and the independence of the transfer property. Ann. Math. Log. 5, 21-46 (1972) · Zbl 0255.02069
[150] Mitchell, W.J.: Aronszajn trees and the independence of the transfer property. Ann. Math. Log. 5, 21-46 (1972/73) · Zbl 0255.02069
[151] Mitchell, W.J.: \[I[\omega_2]I\][ω2] can be the nonstationary ideal on \[\text{ Cof }(\omega_1)\] Cof(ω1). Trans. Am. Math. Soc. 361(2), 561-601 (2009) · Zbl 1179.03048
[152] Monk, J.D.: The size of maximal almost disjoint families. Dissertationes Math. (Rozprawy Mat.), 437, 47 (2006) · Zbl 1107.03058
[153] Moore, G.H.: The origins of forcing. In: Drake, F.R., Truss, J.K. (eds.) Logic Colloquium ’86 (Hull 1986), volume 124 of Studies in Logic and the Foundations of Mathematics, pp. 143-173. North Holland, Amsterdam (1988) · Zbl 1250.03111
[154] Moore, J.T.: A five element basis for the uncountable linear orders. Ann. Math. (2) 163(2), 669-688 (2006) · Zbl 1143.03026
[155] Neeman, I.: Forcing with sequences of models of two types. Notre Dame J. Form. Log. 55(2), 265-298 (2014) · Zbl 1352.03054
[156] Ramsey, F.P.: On a problem of formal logic. Proc. Lond. Math. Soc. S2-30(1), 264-286 (1930) · JFM 55.0032.04
[157] Rinot, A.: Chain conditions of products, and weakly compact cardinals. Bull. Symb. Log. 20(3), 293-314 (2014) · Zbl 1345.03092
[158] Rinot, A.: Chromatic numbers of graphs-large gaps. Combinatorica 35(2), 215-233 (2015) · Zbl 1363.03022
[159] Scott, D.J. (ed.): Axiomatic set theory. Proc. Sympos. Pure Math Vol. XIII, Part I, Univ. Calif., Los Angeles, Calif., 1967. American Mathematical Society, Providence, R.I. (1971) · Zbl 0060.12602
[160] Sharpe, I., Welch, P.D.: Greatly Erdős cardinals with some generalizations to the Chang and Ramsey properties. Ann. Pure Appl. Log. 162(11), 863-902 (2011) · Zbl 1270.03071
[161] Shelah, S.: Independence results. J. Symb. Log. 45(3), 563-573 (1980) · Zbl 0451.03017
[162] Shelah, S.: Proper forcing, volume 940 of Lecture Notes in Mathematics. Springer, Berlin (1982) · Zbl 0495.03035
[163] Shelah, S.: Iterated forcing and normal ideals on \[\omega_1\] ω1. Isr. J. Math. 60(3), 345-380 (1987) · Zbl 0655.03035
[164] Shelah, S.: Reflecting stationary sets and successors of singular cardinals. Arch. Math. Log. 31(1), 25-53 (1991) · Zbl 0742.03017
[165] Shelah, S.: Proper and improper forcing, 2nd edn. Perspectives in Mathematical Logic. Springer, Berlin (1998) · Zbl 0889.03041
[166] Shelah, S., Woodin, H.: Large cardinals imply that every reasonably definable set of reals is Lebesgue measurable. Isr. J. Math. 70(3), 381-394 (1990) · Zbl 0705.03028
[167] Shoenfield, J.R.: Unramified forcing. In: Axiomatic Set Theory (Proc. Sympos. Pure Math., Vol. XIII, Part I, Univ. California, Los Angeles, Calif., 1967), pp. 357-381. Am. Math. Soc., Providence, R.I. (1971) · Zbl 0658.03028
[168] Sierpiński, W.: Sur une décomposition d’ensembles. Monatsh. Math. Phys. 35(1), 239-242 (1928) · JFM 54.0092.01
[169] Sierpiński, W.: Sur un problème de la théorie des relations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (2) 2(3), 285-287 (1933) · JFM 59.0092.01
[170] Sierpiński, W.: Hypothèse du continu. Chelsea Publishing Company, New York, N.Y., 1956. 2nd ed; 1st ed, 1934, Warsaw · Zbl 0009.30201
[171] Silver, J.: Some Applications of Model Theory in Set Theory. PhD thesis, University of California, Berkeley (1966). Advisor R. Vaught · Zbl 1419.54004
[172] Silver, J.: A large cardinal in the constructible universe. Fund. Math. 69, 93-100 (1970) · Zbl 0208.01503
[173] Silver, J.: On the singular cardinals problem. In: Proceedings of the International Congress of Mathematicians (Vancouver, B. C., 1974), vol. 1, pp. 265-268. Canad. Math. Congress, Montreal, Que. (1975) · Zbl 0339.02060
[174] Solovay, R.M.: The measure problem. J. Symb. Log. 29, 227-228 (1964). Abstract for the Association of Symbolic Logic meeting of July 13-17, 1964 held at the University of Bristol; received July 6 (1964)
[175] Solovay, R.M.: A model of set-theory in which every set of reals is Lebesgue measurable. Ann. Math. 2(92), 1-56 (1970) · Zbl 0207.00905
[176] Solovay, R.M.: Real-valued measurable cardinals. In: Axiomatic Set Theory (Proc. Sympos. Pure Math., Vol. XIII, Part I, Univ. California, Los Angeles, Calif., 1967), pp. 397-428. Am. Math. Soc., Providence, R.I. (1971) · Zbl 0719.03025
[177] Solovay, R.M., Reinhardt, W.N., Kanamori, A.: Strong axioms of infinity and elementary embeddings. Ann. Math. Log. 13(1), 73-116 (1978) · Zbl 0376.02055
[178] Solovay, R.M., Tennenbaum, S.: Iterated Cohen extensions and Souslin’s problem. Ann. Math. 2(94), 201-245 (1971) · Zbl 0244.02023
[179] Steel, J.R.: The core model iterability problem, volume 8 of Lecture Notes in Logic. Springer, Berlin (1996) · Zbl 0864.03035
[180] Steel, J.R.: What is \[\dots \]⋯ a Woodin cardinal? Not. Am. Math. Soc. 54(9), 1146-1147 (2007) · Zbl 1153.03315
[181] Suslin, M.: Problème 3. Fund. Math. 1, 223 (1920) · Zbl 0655.03035
[182] Tarski, A.: Quelques théorèmes qui équivalent à l’axiom du choix. Fund. Math. 7, 147-154 (1925)
[183] Tarski, A.: Sur la décomposition des ensembles en sous-ensembles presque disjoints. Fund. Math. 12, 188-205 (1928) · JFM 54.0092.02
[184] Tarski, A.: Sur la décomposition des ensembles en sous-ensembles presque disjoints (supplément). Fund. Math. 14, 205-215 (1929) · JFM 55.0053.04
[185] Tarski, A.: Ideale in vollstädigen Mengenkörpern, ii. Fund. Math. 33, 51-65 (1945) · Zbl 0060.13306
[186] Tennenbaum, S.: Souslin’s problem. Proc. Nat. Acad. Sci. USA 59, 60-63 (1968) · Zbl 0172.29503
[187] Todorcevic, S.: Some consequences of \[{\rm MA}+\lnot{\rm wKH}\] MA+¬wKH. Topol. Appl. 12(2), 187-202 (1981) · Zbl 0464.54004
[188] Todorcevic, S.: Forcing positive partition relations. Trans. Am. Math. Soc. 280(2), 703-720 (1983) · Zbl 0532.03023
[189] Todorcevic, S.: A note on the proper forcing axiom. In: Baumgartner, J.E., Martin, D.A., Shelah, S. (eds.) Axiomatic Set Theory, Volume 31 of Contemporary Mathematics, pp. 209-218. American Mathematical Society (1984) · Zbl 0564.03038
[190] Todorcevic, S.: Trees and linearly ordered sets. In: Handbook of Set-Theoretic Topology, pp. 235-293. North-Holland, Amsterdam (1984) · Zbl 0557.54021
[191] Todorcevic, S.: Partition relations for partially ordered sets. Acta Math. 155(1-2), 1-25 (1985) · Zbl 0603.03013
[192] Todorcevic, S.: Partitioning pairs of countable ordinals. Acta Math. 159(3-4), 261-294 (1987) · Zbl 0658.03028
[193] Todorcevic, S.: Partition Problems in Topology, volume 84 of Contemporary Mathematics. American Mathematical Society, Providence, RI (1989) · Zbl 0659.54001
[194] Todorcevic, S.: Comparing the continuum with the first two uncountable cardinals. In: Logic and Scientific Methods (Florence, 1995), volume 259 of Synthese Lib., pp. 145-155. Kluwer Acad. Publ., Dordrecht (1997) · Zbl 0906.03050
[195] Ulam, S.: Zur masstheorie in der allgemeinen mengenlehre. Fund. Math. 16(1), 140-150 (1930) · JFM 56.0920.04
[196] Veličković, B.: Forcing axioms and stationary sets. Adv. Math. 94(2), 256-284 (1992) · Zbl 0785.03031
[197] Velickovic, B.; Venturi, G., Proper forcing remastered, 331-362 (2013), Cambridge · Zbl 1367.03094
[198] Viale, M., Weiß, C.: On the consistency strength of the proper forcing axiom. Adv. Math. 228(5), 2672-2687 (2011) · Zbl 1251.03059
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.