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The life and work of Bohuslav Balcar (1943–2017). (English) Zbl 1424.01013


MSC:

01A70 Biographies, obituaries, personalia, bibliographies

Biographic References:

Balcar, Bohuslav
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[1] Balcar B.; Jech T., Models of the theory of sets generated by a perfect relation, Časopis Pěst. Mat. 90 (1965), 413-434 (Russian. Czech, German summary)
[2] Balcar B.; Slavíček S., Computer minimization of incompletely specified logical functions, Apl. Mat. 11 (1966), no. 4, 278-282 (Czech) · Zbl 0141.14404
[3] Vopěnka P.; Balcar B., Generator classes in set theory, Z. Math. Logik Grundlagen Math. 13 (1967), 97-98 · Zbl 0153.01502 · doi:10.1002/malq.19670130702
[4] Vopěnka P.; Balcar B., On complete models of the set theory, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 15 (1967), 839-841 · Zbl 0177.01404
[5] Vopěnka P.; Balcar B.; Hájek P., The notion of effective sets and a new proof of the consistency of the axiom of choice, J. Symbolic Logic 33 (1968), no. 3, 495-496
[6] Balcar B.; Hájek P., Description of the hypothetical computing machine AIC for automatic processing of curves, Československá fyziologie 18 (1969), no. 2, 151-154 (Czech)
[7] Balcar B.; Sochor A., The general theory of semisets. Syntactic models of the set theory, Aspects of Math. Logic, C.I.M.E., Varenna, 1968, Edizioni Cremonese, Rome, 1969, 267-285
[8] Balcar B.; Vopěnka P., On systems of almost disjoint sets, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 20 (1972), 421-424 · Zbl 0245.04002
[9] Balcar B., A theorem on supports in the theory of semisets, Prepared for publication by P. Hájek, Comment. Math. Univ. Carolinae 14 (1973), no. 1, 1-6 · Zbl 0281.02060
[10] Balcar B.; Guzicki W., A remark on powers of singular cardinals, Set Theory and Hierarchy Theory, Proc. Second Conf., Bierutowice, 1975, Lecture Notes in Math., 537, Springer, Berlin, 1976, pages 25-28 · Zbl 0356.02047 · doi:10.1007/BFb0096890
[11] Balcar B.; Vojtáš P., Refining systems on Boolean algebras, Set Theory and Hierarchy Theory, V, Proc. Third Conf., Bierutowice, 1976, Lecture Notes in Math., 619, Springer, Berlin, 1977, pages 45-48 · doi:10.1007/BFb0067641
[12] Balcar B.; Štěpánek P., Boolean matrices, subalgebras and automorphisms of complete Boolean algebras, Fund. Math. 96 (1977), no. 3, 211-223 · Zbl 0375.06010 · doi:10.4064/fm-96-3-211-223
[13] Štěpánek P.; Balcar B., Embedding theorems for Boolean algebras and consistency results on ordinal definable sets, J. Symbolic Logic 42 (1977), no. 1, 64-76 · Zbl 0369.02039 · doi:10.2307/2272320
[14] Balcar B.; Frankiewicz R., To distinguish topologically the spaces \(m^{⁎} \), II, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 26 (1978), no. 6, 521-523 · Zbl 0397.54010
[15] Balcar B.; Hájek P., On sequences of degrees of constructibility, Z. Math. Logik Grundlagen Math. 24 (1978), no. 4, 291-296 · Zbl 0414.03032 · doi:10.1002/malq.19780241903
[16] Balcar B.; Frankiewicz R., Ultrafilters and \(ω _{1}\)-points in \(β N⧵\textbf{N}\), Bull. Acad. Polon. Sci. Sér. Sci. Math. 27 (1979), no. 7-8, 593-598 · Zbl 0429.54002
[17] Balcar B.; Frankiewicz R.; Mills Ch., More on nowhere dense closed \(P\)-sets, Bull. Acad. Polon. Sci. Sér. Sci. Math. 28 (1980), no. 5-6, 295-299 · Zbl 0467.54024
[18] Balcar B.; Pelant J.; Simon P., The space of ultrafilters on \(N\) covered by nowhere dense sets, Fund. Math. 110 (1980), no. 1, 11-24 · Zbl 0568.54004 · doi:10.4064/fm-110-1-11-24
[19] Balcar B.; Simon P.; Vojtáš P., Refinement and properties and extending of filters, Bull. Acad. Polon. Sci. Sér. Sci. Math. 28 (1980), no. 11-12, 530-540
[20] Balcar B.; Vojtáš P., Almost disjoint refinement of families of subsets of \(N\), Proc. Amer. Math. Soc. 79 (1980), no. 3, 465-470 · Zbl 0443.04005
[21] Balcar B.; Simon P.; Vojtáš P., Refinement properties and extensions of filters in Boolean algebras, Trans. Amer. Math. Soc. 267 (1981), no. 1, 265-283 · Zbl 0498.04007 · doi:10.1090/S0002-9947-1981-0621987-0
[22] Balcar B.; Franěk F., Independent families in complete Boolean algebras, Trans. Amer. Math. Soc. 274 (1982), no. 2, 607-618 · Zbl 0527.06008 · doi:10.1090/S0002-9947-1982-0675069-3
[23] Balcar B.; Simon P., Strong decomposability of ultrafilters I, Logic Colloq. ’80, Praha, 1980, Stud. Logic Foundations Math., 108, North-Holland, Amsterdam, 1982, pages 1-10
[24] Balcar B.; Simon P., Cardinal invariants in Boolean spaces, General Topology and Its Relations to Modern Analysis and Algebra, V, Praha, 1981, Sigma Ser. Pure Math., 3, Heldermann, Berlin, 1983, pages 39-47
[25] Balcar B.; Dočkálková J.; Simon P., Almost disjoint families of countable sets, Finite and Infinite Sets, Vol. I, II, Eger, 1981, Colloq. Math. Soc. János Bolyai, North-Holland, Amsterdam, 1984, pages 59-88
[26] Balcar B.; Štěpánek P., Set Theory, Academia [Publishing House of the Czech Academy of Sciences], Praha, 1986 (Czech) · Zbl 0635.03039
[27] Balcar B.; Franek F., Completion of factor algebras of ideals, Proc. Amer. Math. Soc. 100 (1987), no. 2, 205-212 · Zbl 0618.06008 · doi:10.1090/S0002-9939-1987-0884452-2
[28] Balcar B.; Kalášek P.; Williams S. W., On the multiple Birkhoff recurrence theorem in dynamics, Comment. Math. Univ. Carolin. 28 (1987), no. 4, 607-612 · Zbl 0642.54037
[29] Balcar B.; Simon P., On collections of almost disjoint families, Comment. Math. Univ. Carolin. 29 (1988), no. 4, 631-646 · Zbl 0675.03029
[30] Balcar B.; Kalášek P., Nonexistence of multiple recurrent point in the ultrafilter dynamical system, Bull. Polish Acad. Sci. Math. 37 (1989), no. 7-12, 525-529 · Zbl 0759.54024
[31] Balcar B.; Simon P., Appendix on general topology, Handbook of Boolean Algebras, Vol. 3, North-Holland, Amsterdam, 1989, pages 1239-1267
[32] Balcar B.; Simon P., Chart of topological duality, Handbook of Boolean algebras, Vol. 3, North-Holland, Amsterdam, 1989, pages 1236-1237
[33] Balcar B.; Simon P., Disjoint refinement, Handbook of Boolean Algebras, Vol. 2, North-Holland, Amsterdam, 1989, pages 333-388
[34] Balcar B.; Błaszczyk A., On minimal dynamical systems on Boolean algebras, Comment. Math. Univ. Carolin. 31 (1990), no. 1, 7-11 · Zbl 0697.54021
[35] Balcar B.; Dow A., Dynamical systems on compact extremally disconnected spaces, Topology Appl. 41 (1991), no. 1-2, 41-56 · Zbl 0766.54037 · doi:10.1016/0166-8641(91)90099-8
[36] Balcar B.; Simon P., On minimal \(π\)-character of points in extremally disconnected compact spaces, Topology Appl. 41 (1991), no. 1-2, 133-145 · Zbl 0752.54013 · doi:10.1016/0166-8641(91)90105-U
[37] Balcar B.; Simon P., Reaping number and \(π\)-character of Boolean algebras, Topological, Algebraical and Combinatorial Structures, Frolík’s memorial volume, Discrete Math. 108 (1992), no. 1-3, 5-12 · Zbl 0766.06012
[38] Balcar B.; Simon P., Baire number of the spaces of uniform ultrafilters, Israel J. Math. 92 (1995), no. 1-3, 263-272 · Zbl 0834.54001 · doi:10.1007/BF02762081
[39] Balcar B.; Franek F., Structural properties of universal minimal dynamical systems for discrete semigroups, Trans. Amer. Math. Soc. 349 (1997), no. 5, 1697-1724 · Zbl 0867.54038 · doi:10.1090/S0002-9947-97-01868-0
[40] Balcar B.; Jech T.; Zapletal J., Semi-Cohen Boolean algebras, Ann. Pure Appl. Logic 87 (1997), no. 3, 187-208 · Zbl 0886.03036 · doi:10.1016/S0168-0072(97)00009-2
[41] Balcar B.; Główczyński W.; Jech T., The sequential topology on complete Boolean algebras, Fund. Math. 155 (1998), no. 1, 59-78 · Zbl 0910.28004
[42] Balcar B.; Franek F.; Hruška J., Exhaustive zero-convergence structures on Boolean algebras, Acta Univ. Carolin. Math. Phys. 40 (1999), no. 2, 27-41 · Zbl 0969.06011
[43] Balcar B.; Hušek M., Sequential continuity and submeasurable cardinals, Proc. of the International School of Mathematics “G. Stampacchia”, Erice, 1998, Topology Appl. 111 (2001), no. 1-2, pages 49-58 · Zbl 0971.03049 · doi:10.1016/S0166-8641(99)00197-2
[44] Balcar B.; Simon P., The name for Kojman-Shelah collapsing function, Dedicated to Petr Vopěnka, Ann. Pure Appl. Logic 109 (2001), no. 1-2, 131-137 · Zbl 0989.03051 · doi:10.1016/S0168-0072(01)00046-X
[45] Balcar B.; Copláková E., Zero-dimensional spaces, Encyclopedia of General Topology, (Hart K. P., Nagata J., Vaughan J. E., eds.) Elsevier Science Publishers, Amsterdam, 2004, pages 323-325
[46] Balcar B.; Hernández-Hernández F.; Hrušák M., Combinatorics of dense subsets of the rationals, Fund. Math. 183 (2004), no. 1, 59-80 · Zbl 1051.03038 · doi:10.4064/fm183-1-4
[47] Balcar B.; Hrušák M., Distributivity of the algebra of regular open subsets of {\(β\mathbb R⧵ \mathbb R\), }, Topology Appl. 149 (2005), no. 1-3, 1-7 · Zbl 1071.54018 · doi:10.1016/j.topol.2004.08.009
[48] Balcar B.; Jech T.; Pazák T., Complete CCC Boolean algebras, the order sequential topology, and a problem of von Neumann, Bull. London Math. Soc. 37 (2005), no. 6, 885-898 · Zbl 1101.28003 · doi:10.1112/S0024609305004807
[49] Balcar B.; Jech T., Weak distributivity, a problem of von Neumann and the mystery of measurability, Bull. Symbolic Logic 12 (2006), no. 2, 241-266 · Zbl 1120.03028 · doi:10.2178/bsl/1146620061
[50] Balcar B.; Jech T., Contributions to the theory of weakly distributive complete Boolean algebras, Andrzej Mostowski and Foundational Studies, IOS, Amsterdam, 2008, 144-150 · Zbl 1146.03036
[51] Balcar B.; Pazák T., Quotients of Boolean algebras and regular subalgebras, Arch. Math. Logic 49 (2010), no. 3, 329-342 · Zbl 1196.03065 · doi:10.1007/s00153-010-0174-y
[52] Balcar B.; Doucha M.; Hrušák M., Base tree property, Order 32 (2015), no. 1, 69-81 · Zbl 1321.06002 · doi:10.1007/s11083-013-9316-2
[53] Balcar B.; Pazák T.; Thümmel E., On Todorcevic orderings, Fund. Math. 228 (2015), no. 2, 173-192 · Zbl 1373.03072 · doi:10.4064/fm228-2-4
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