{"id":19,"date":"2012-09-05T11:22:25","date_gmt":"2012-09-05T15:22:25","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/template\/?page_id=19"},"modified":"2026-03-19T08:13:41","modified_gmt":"2026-03-19T12:13:41","slug":"publications","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/zapletal\/publications\/","title":{"rendered":"Publications"},"content":{"rendered":"\r\n
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Publications<\/h1>\n\n\n\n

\u00a0Independence relations in the Solovay model II<\/a>\u00a0 A completely preliminary version. This paper develops the theory of balanced forcing in a purely geometric framework, and it discusses many weak independence relations useful in this context.<\/p>\n\n\n\n\n\n

Independence relations in the Solovay model I<\/a>. This paper sets up a “geometric” axiomatization of the Solovay model and provides clean, forcing-free and descriptive set theory-free proofs of many classical results in that model.<\/p>\n\n\n\n\n\n

Dynamical ideals and the axiom of choice<\/a>. This paper isolates several properties of dynamical ideals and shows how they are reflected in the associated permutation models of ZF.<\/p>\n\n\n\n\n\n

Classifying open subgroups of non-archimedean groups\u00a0<\/a>\u00a0 a completely preliminary version.<\/p>\n\n\n\n\n\n

Triangles and Vitali sets<\/a> It is consistent with ZF+DC that the hypergraph of equilateral triangles in the plane has countable chromatic number while there is no Vitali set.<\/p>\n\n\n\n\n\n

\u00a0Coloring equilateral triangles<\/a>. I show it consistent with ZF+DC that the hypergraph of equilateral triangles in Rn has countable chromatic number while the hypergraph of isosceles triangles in R2 does not, this for any number n>0.<\/p>\n\n\n\n\n\n

Two graph games<\/a>, with David Chodounsky, submitted to Electronic Journal of Combinatorics. We identify two determined games which can be used to prove that certain sigma-algebraic graphs have countable chromatic number.<\/p>\n\n\n\n\n\n

Coloring closed Noetherian graphs<\/a>, Journal of Mathematical Logic, in print. I show that for every algebraic graph on a Euclidean space, either it has a perfect clique or it is consistent with ZF+DC that it has countable chromatic number and Vitali set does not exist.<\/p>\n\n\n\n\n\n

Coloring the distance graphs<\/a> Eur. J. Math.<\/span><\/a>\u00a09\u00a0<\/a><\/span>(<\/span>2023<\/a><\/span>)<\/span><\/span>, no.\u00a03<\/span><\/a><\/span>, 66<\/span>. For every n>0, let Gn be the graph on n-dimensional Euclidean space connecting points of rational distance. It is consistent with ZF+DC that the chromatic number of Gn is countable while the chromatic number of Gn+1 is not.<\/p>\n\n\n\n\n\n

Coloring triangles and rectangles\u00a0<\/a>\u00a0 accepted to Commentationes Mathematicae Universitatis Carolinae. It is consistent with ZF+DC that the chromatic number of the rectangle hypergraph in n dimensions is countable while the chromatic number of equilateral triangles in two dimensions is uncountable.<\/p>\n\n\n\n\n\n

Krull dimension in set theory \u00a0<\/a>Ann. Pure Appl. Logic<\/span><\/a>\u00a0174\u00a0<\/a>(<\/span>2023<\/a><\/span>)<\/span><\/span>, no.\u00a09<\/span><\/a><\/span>, Paper No. 103299, 16 pp<\/span>. For every n>0, let Dn be the hypergraph of all rectangles on n-dimensional Euclidean space. It is consistent with ZF+DC that the chromatic number of Gn is countable while the chromatic number of Gn+1 is not.<\/p>\n\n\n\n\n\n

Polar forcings and measured extensions<\/a>, with Paul Larson. Topology Appl. 323 (2023), Paper No. 108290, 12 pp. A sigma-ideal on a Polish space is polar if it is the intersection of null ideals of some collection of measures. We analyze the quotient forcings obtained by such ideals and prove iteration and preservation theorems for them.<\/p>\n\n\n\n\n\n

Sequential topologies and Dedekind finite sets<\/a> MLQ Math. Log. Q. 68 (2022), no. 1, 107\u2013109. It is consistent with ZF that the topology of real numbers is not sequential while every infinite set of reals contains a countable infinite subset.<\/p>\n\n\n\n

Set theory and foundations of mathematics\u2014an introduction to mathematical logic. Vol. II. Foundations of mathematics. Cenzer, Douglas; Larson, Jean; Porter, Christopher; Zapletal, Jind\u0159ich. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2022, xiii+239 pp. ISBN: 978-981-124-384-4; 978-981-124-385-1; 978-981-124-386-8<\/p>\n\n\n\n

Set theory and foundations of mathematics\u2014an introduction to mathematical logic. Vol. 1. Set theory. Cenzer, Douglas; Larson, Jean; Porter, Christopher; Zapletal, Jindrich. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2020, xi+209 pp. ISBN: 978-981-120-193-6; 978-981-120-192-9; 978-981-120-194-3<\/p>\n\n\n\n

Structure and randomness in computability and set theory. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2021, xx+366 pp. ISBN: [9789813228221]; [9789813228238]; [9789813228245]<\/p>\n\n\n\n

Coloring the distance graphs in three dimensions <\/a>submitted to Combinatorica.\u00a0For every n>0, let Gn be the graph on n-dimensional Euclidean space connecting points of rational distance. It is consistent with ZF+DC that the chromatic number of G3 is countable while the chromatic number of G4 is not.<\/p>\n\n\n\n\n\n

Transcendental pairs of generic extensions<\/a><\/p>\n\n\n\n\n\n

Noetherian spaces in choiceless set theory\u00a0<\/a>It is consistent with ZF+DC that every K sigma Polish field has a transcendence basis over a countable subfield, yet there is no nonprincipal ultrafilter over the natural numbers, the Lebesgue null ideal is closed under well-ordered unions etc. There are many independence results obtained by the same method.<\/p>\n\n\n\n\n\n

Subadditive families of hypergraphs\u00a0<\/a>Accepted to Annals of Pure and Applied Logic. For proper forcings defined from a family of hypergraphs on a Polish space, I provide a simple combinatorial criterion on the hypergraphs equivalent to the forcing not adding an independent real.<\/p>\n\n\n\n\n\n

Geometric set theory, with Paul Larson. AMS Surveys and Monographs 248<\/p>\n\n\n\n\n\n

Hypergraphs and proper forcing<\/a> Journal of Mathematical Logic Vol. 19, No. 02, 1950007 (2019) For a countable family of analytic hypergraphs on a Polish space, consider the sigma-ideal generated by Borel sets which are anticliques with respect to one of them. It turns out that many forcings can be obtained as quotient forcings of such sigma-ideals, there is a close connection between combinatorial properties of the hypergraphs and preservation properties of the forcings, and one can prove suitable iteration and product forcing theorems.<\/p>\n\n\n\n\n\n

Namba forcing axiom may fail<\/a>, Mathematical Logic Quarterly (2018), https:\/\/doi.org\/10.1002\/malq.201700025<\/p>\n\n\n\n\n\n

Cardinal invariants of closed graphs<\/a>, with Francis Adams, Israel Journal of Mathematics, (2018), https:\/\/doi.org\/10.1007\/s11856-018-1745-6<\/p>\n\n\n\n\n\n

Strong measure zero sets in Polish groups<\/a>, with Michael Hrusak, Illinois Journal of Mathematics 60 (2016), Number 3-4, 751-760<\/p>\n\n\n\n\n\n

Canonical models for fragments of the axiom of choice<\/a>, with Paul Larson, Journal of Symbolic Logic 82 (2017) 2, 489-509<\/p>\n\n\n\n\n\n

Ramsey ultrafilters and countable-to-one uniformization, with Richard Ketchersid and Paul Larson, Topology and Its Applications 213 (2016), 190–198<\/p>\n\n\n\n\n\n

Interpreter for topologists<\/a>, Journal of Logic and Analysis 7 (2015), 1-61<\/p>\n\n\n\n\n\n

Why Y-c.c.<\/a>, with David Chodounsky, Annals of Pure and Applied Logic 166 (2015) 1123-1149<\/p>\n\n\n\n\n\n

Dimension theory and forcing<\/a>, <\/a>Topology and Its Applications 167 (2014) 31-35<\/p>\n\n\n\n\n\n

Cofinalities of Borel ideals<\/a>, with Michael Hrusak and Diego Rojas Rebolledo, Mathematical Logic Quarterly 1-9 (2014) DOI 101002\/malq.201200079<\/p>\n\n\n\n\n\n

Separation problems and forcing<\/a>.<\/span> J. Math. Log.<\/em><\/a> 13 <\/a> (2013), <\/a> no. 1,<\/a> 1350002<\/p>\n\n\n\n\n\n

Canonical Ramsey theory on Polish spaces<\/a>, with Marcin Sabok and Vladimir Kanovei, Cambridge Tracts in Mathematics 202, Cambridge University Press 2013, ISBN 978-1-107-02685-8<\/p>\n\n\n\n\n\n

On the Steinhaus and Bergman properties for infinite products of finite groups<\/a>,<\/span> with Simon Thomas,\u00a0 Confluentes Math.<\/em><\/a> 4 <\/a> (2012), <\/a> no. 2,<\/a> 1250002<\/p>\n\n\n\n\n\n

Pinned equivalence relations<\/a>, Mathematical Research Letters 18 (2011) 559-564<\/p>\n\n\n\n\n\n

More ideals with the Komjath-Laczkovich property<\/a>, Topology and Its Applications 158 (2011) 1149-1156<\/p>\n\n\n\n\n\n

Forcing properties of ideals of closed sets<\/a>, with Marcin Sabok, J. Symbolic Logic 76 (2011) 1075–1095<\/p>\n\n\n\n\n\n

Ramsey theorem for product of finite sets with submeasures<\/a>, with Saharon Shelah, Combinatorica 31 (2011) 225-244<\/p>\n\n\n\n\n\n

On the existence of a sigma-closed dense subset<\/a>, Comment.Math.Univ.Carolin. 51,3 (2010) 513-517<\/p>\n\n\n\n\n\n

Applications of the ergodic iteration theorem<\/a>. Math. Log. Q. 56 (2010), no. 2, 116-125<\/p>\n\n\n\n\n\n

Regular embeddings of the stationary tower and Woodin’s\u00a0\u221122 maximality theorem<\/a>, with Richard Ketchersid and Paul Larson, J. Symbolic Logic 75 (2010), no. 2, 711-727<\/p>\n\n\n\n\n\n

Preserving P-points in definable forcing<\/a>. Fund. Math. 204 (2009), no. 2, 145-154<\/p>\n\n\n\n\n\n

Increasing\u00a0\u039412 by a Namba-style forcing<\/a>, with Richard Ketchersid and Paul Larson, J. Symbolic Logic 72 (2007), 1372–1378<\/p>\n\n\n\n\n\n

On the structure of stationary sets<\/a>, with Qi Feng and Thomas Jech, Sci. China Ser. A 50 (2007) 615-627<\/p>\n\n\n\n\n\n

Forcing with quotients<\/a>, with Michael Hrusak, Archive Math. Logic 47 (2008), 719-739<\/p>\n\n\n\n\n\n

Forcing idealized<\/a>, Cambridge Tracts in Mathematics 174, Cambridge University Press 2008, ISBN 9780521874267<\/p>\n\n\n\n\n\n

Proper forcing and rectangular Ramsey theorems, Israel J. Math. 152 (2006), 29–47<\/p>\n\n\n\n\n\n

Between Maharam’s and von Neumann’s problem, with Ilijas Farah, Math. Research Letters 11 (2004), 673–684<\/p>\n\n\n\n\n\n

Four and more<\/a>, Ann. Pure Appl. Logic, with Ilijas Farah, Ann. Pure Appl. Logic 140 (2006), 3–39<\/p>\n\n\n\n\n\n

Descriptive set theory and definable forcing, Memoirs Amer. Math. Soc. 793 (2004)<\/p>\n\n\n\n\n\n

Games with creatures<\/a>, with S. Shelah, Comm. Math. Univ. Carolinae 44 (2003), 9–23<\/p>\n\n\n\n\n\n

Duality and the PCF theory, with S. Shelah, Math. Research Letters 9 (2002), 585–595<\/p>\n\n\n\n\n\n

Forcing with ideals of closed sets, Comm. Math. Univ. Carolinae 43,1 (2002), 181–188<\/p>\n\n\n\n\n\n

Isolating cardinal invariants, J. Math. Logic, 2003, 143-162<\/p>\n\n\n\n\n\n

Terminal notions in set theory<\/a>, Ann. Pure Appl. Logic 109 (2001), 89–116<\/p>\n\n\n\n\n\n

Transfinite open games, Topology and Its Applications 111 (2001), 289–297<\/p>\n\n\n\n\n\n

Killing ideals and adding reals, J. Symbolic Logic 65 (2000), 747–755<\/p>\n\n\n\n\n\n

The nonstationary ideal and the other sigma ideals on omega one, Trans. Amer. Math. Soc. 352 (2000), 3981–3993<\/p>\n\n\n\n\n\n

Terminal notions, Bull. Symbolic Logic 5 (1999), 470–484<\/p>\n\n\n\n\n\n

On the Alaoglu-Birkhoff equivalence of posets, with S. Todorcevic, Illinois J. Math. 43 (1999), 281–292<\/p>\n\n\n\n\n\n

Canonical models for aleph one combinatorics, with S. Shelah, Ann. Pure Appl. Logic 98 (1999), 217–259<\/p>\n\n\n\n\n\n

Proper forcing and absoluteness in L(R), with I. Neeman, Comm. Math. Univ. Carolinae 39 (1998), 281–301<\/p>\n\n\n\n\n\n

A dichotomy for forcing notions, Math. Res. Lett. 5 (1998) 213–226<\/p>\n\n\n\n\n\n

Preserving sigma-ideals, J. Symbolic Logic 63 (1998), 1437–1441<\/p>\n\n\n\n\n\n

Keeping additivity of the null ideal small, Proc. Amer. Math. Soc. 125 (1997), 2443–2451<\/p>\n\n\n\n\n\n

Embeddings of Cohen algebras, with S. Shelah, Adv. Math. 126 (1997), 93–119<\/p>\n\n\n\n\n\n

Semi-Cohen boolean algebras, with B. Balcar and T. Jech, Ann. Pure Appl. Logic 87 (1997), 187–208<\/p>\n\n\n\n\n\n

Strongly almost disjoint functions, Israel J. Math. 97 (1997), 101–111<\/p>\n\n\n\n\n\n

Small forcings and Cohen reals, J. Symbolic Logic 62 (1997), 280–284<\/p>\n\n\n\n\n\n

Splitting number at uncountable cardinals, J. Symbolic Logic 62 (1997), 35–42<\/p>\n\n\n\n\n\n

A classification of definable partial orders on omega one, Fund. Math. 153 (1997), 141-144<\/p>\n\n\n\n\n\n

Characterization of the club forcing, in Papers on General Topology and Applications, S. Andima, R. Flagg, G. Itzkowitz,<\/p>\n\n\n\n\n\n

Y. Kong, R. Kopperman amd P. Misra, eds., Annals of the New York Academy of Sciences 806 (1996), 476–484<\/p>\n\n\n\n\n\n

A new proof of Kunen inconsistency, Proc. Amer. Math. Soc. 124 (1996), 2203-2205<\/p>\n\n\n\n\n\n

More on the cut and choose game, Ann. Pure Appl. Logic 76 (1995), 291–301<\/p>\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":251,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-19","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/zapletal\/wp-json\/wp\/v2\/pages\/19","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/zapletal\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/zapletal\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/zapletal\/wp-json\/wp\/v2\/users\/251"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/zapletal\/wp-json\/wp\/v2\/comments?post=19"}],"version-history":[{"count":11,"href":"https:\/\/people.clas.ufl.edu\/zapletal\/wp-json\/wp\/v2\/pages\/19\/revisions"}],"predecessor-version":[{"id":1797,"href":"https:\/\/people.clas.ufl.edu\/zapletal\/wp-json\/wp\/v2\/pages\/19\/revisions\/1797"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/zapletal\/wp-json\/wp\/v2\/media?parent=19"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}