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Grants
Principal Investigator: Czech Science Foundation (GACR), The role of set theory in modern mathematics, 24-12141S. (2024-2026)
Principal Investigator: Mobility/Aktion Grant Czech Republic (FFUK, Department of Logic) – Austria, Vienna
(Department of Mathematics, V. Fischer), Compactness and cardinal invariants, 8J23AT015. (2023-2024)
Principal investigator (with V. Fischer for FWF): Joint Lead-Agency research grant between Austrian Science Foundation (FWF) and Czech Science Foundation (GACR), Compactness principles and combinatorics, 19-29633L. (2019-2021)
Principal Investigator: Mobility/Aktion Grant Czech Republic (FFUK, Department of Logic) – Austria, Vienna
(KGRC), Compactness and Cantor space, 8J19AT033. (2019-2020)
Principal investigator (with Sy Friedman for FWF): Joint Lead-Agency research grant between Austrian Science Foundation (FWF) and Czech Science Foundation (GACR), no I 1921-N25, The continuum, forcing, and large cardinals. (2015-2017)
Postdoc at Kurt Goedel Research Center, Vienna. (2013-2015)
Principal Investigator: Mobility/Aktion Grant Czech Republic (FFUK, Department of Logic) – Austria, Vienna
(KGRC), Definability and Ideals, MEB061106. (2010-2012)
Principal investigator: Postdoctoral grant by Czech Science Foundation (GACR), no. 201/09/P115. (2008-2011)
Submitted papers
(joint with O. Ježil and M. Narusevych) Forcing in bounded arithmetic and set theory: analogies and differences, submitted 2026, [Arxiv]
Rado’s Conjecture and the random algebra, submitted 2026,
[Arxiv]
Forcing with random variables in bounded arithmetics and set theory, submitted 2026,
[Arxiv]
Compactness for small cardinals in mathematics: principles, consequences, and limitations, submitted 2025,
[Arxiv]
Publikace
Honzík R., Stejskalová Š.: Generalized cardinal invariants for an inaccessible κ with compactness at κ++. Archive for Mathematical Logic, 2025, č. • no. 64, s. • p. 1077-1102. ISSN 0933-5846.
Honzík R.: On lifting of embeddings between transitive models of set theory. Acta Universitatis Carolinae. Philosophica et Historica, 2025, č. • no. 2022, s. • p. 27-45. ISSN 0567-8293.
Honzík R.: The Rabin-Keisler theorem and the sizes of ultrapowers. Acta Universitatis Carolinae. Philosophica et Historica, 2025, č. • no. 2022, s. • p. 45-55. ISSN 0567-8293.
Honzík R., Lambie-Hanson C., Stejskalová Š.: Indestructibility of some compactness principles over models of PFA*. Annals of Pure and Applied Logic, 2024, č. • no. 175. ISSN 0168-0072.
Habic M., Honzík R.: Capturing sets of ordinals by normal ultrapowers. Annals of Pure and Applied Logic, 2023, č. • no. 174. ISSN 0168-0072.
Honzík R., Stejskalová Š.: Small u(kappa) at singular kappa with compactness at kappa(++). Archive for Mathematical Logic, 2022, č. • no. 61, s. • p. 33-54. ISSN 0933-5846.
Honzík R., Stejskalová Š.: The tree property at aleph_{omega 2} with a finite gap. Fundamenta Mathematicae, 2020, č. • no. 251, s. • p. 219-244. ISSN 0016-2736.
Honzík R., Stejskalová Š.: INDESTRUCTIBILITY OF THE TREE PROPERTY. Journal of Symbolic Logic, 2020, č. • no. 85, s. • p. 467-485. ISSN 0022-4812.
Honzík R.: A Laver-like indestructibility for hypermeasurable cardinals. Archive for Mathematical Logic, 2019, č. • no. 58, s. • p. 275-287. ISSN 0933-5846.
Friedman S., Honzík R., Stejskalová Š.: The tree property at the double successor of a singular cardinal with a larger gap. Annals of Pure and Applied Logic, 2018, č. • no. 2018, s. • p. 548-564. ISSN 0168-0072.
Honzík R., Antos C., Friedman S., Ternullo C.: The Hyperuniverse Project and Maximality. Neuveden, Birkhäuser Basel, 2018. 270 s. • p. ISBN 978-3-319-62934-6.
Honzík R., Stejskalová Š.: The tree property and the continuum function below aleph_omega. Mathematical Logic Quarterly, 2018, č. • no. 2018, s. • p. 89-102. ISSN 0942-5616.
Honzík R.: Preserving measurability with Cohen iterations. Acta Universitatis Carolinae. Philosophica et Historica, 2017, č. • no. 2017, s. • p. 27-32. ISSN 0567-8293.
Honzík R., Friedman S.: Definability of satisfaction in outer models. Journal of Symbolic Logic, 2016, č. • no. 81, s. • p. 1047-1068. ISSN 0022-4812.
Honzík R., Friedman S.: On strong forms of reflection in set theory. Mathematical Logic Quarterly, 2016, č. • no. 62, s. • p. 52-58. ISSN 0942-5616.
Honzík R., Stejskalová Š.: A survey of special Aronszajn trees. Acta Universitatis Carolinae. Philosophica et Historica, 2016, č. • no. 1, s. • p. 73-91. ISSN 0567-8293.
Honzík R., Verner J.: A lifting argument for generalized Gregorieff forcing. Notre Dame Journal of Formal Logic, 2016, č. • no. 2016, s. • p. 221-231. ISSN 0029-4527.
Honzík R.: Large cardinals and their effect on the continuum function on regular cardinals. Acta Universitatis Carolinae. Philosophica et Historica, 2016, č. • no. 1, s. • p. 55-72. ISSN 0567-8293.
Antos C., Friedman S., Honzík R., Ternullo C.: Multiverse conceptions in set theory. Synthese, 2015, č. • no. 192, s. • p. 2463-2488. ISSN 0039-7857.
Friedman S., Honzík R.: The tree property at the aleph_2n's and the failure of SCH at aleph_omega. Annals of Pure and Applied Logic, 2015, č. • no. 166, s. • p. 526-552. ISSN 0168-0072.
Cody B., Friedman S., Honzík R.: Easton functions and supercompactness. Fundamenta Mathematicae, 2014, č. • no. 226, s. • p. 279-296. ISSN 0016-2736.
Friedman S., Honzík R., Zdomskyy L.: Fusion and large cardinal preservation. Annals of Pure and Applied Logic, 2013, č. • no. 164, s. • p. 1247-1273. ISSN 0168-0072.
Honzík R.: Large Cardinals and the Continuum Hypothesis. Acta Universitatis Carolinae. Philosophica et Historica, 2013, č. • no. 2010, s. • p. 35-52. ISSN 0567-8293.
Honzík R.: Supercompactness and Failures of GCH. Fundamenta Mathematicae, 2012, č. • no. 219, s. • p. 15-36. ISSN 0016-2736.
Honzík R.: A definable failure of the Singular Cardinal Hypothesis. Israel Journal of Mathematics, 2012, č. • no. 192, s. • p. 719-762. ISSN 0021-2172.
Honzík R.: Easton's theorem and large cardinals from the optimal hypothesis. Annals of Pure and Applied Logic, 2012, č. • no. 163, s. • p. 1738-1747. ISSN 0168-0072.
Honzík R.: A characterization of lifting generics for Sacks-like forcings. Acta Universitatis Carolinae. Mathematica et Physica, 2010, č. • no. 51, s. • p. 49-55. ISSN 0001-7140.
Honzík R.: Global Singularization and the Failure of SCH. Annals of Pure and Applied Logic, 2010, č. • no. 161, s. • p. 895-915. ISSN 0168-0072.
orcid.org/0000-0003-0834-0053
