Doc. Radek Honzik, Ph.D.
Professor at Charles University, Faculty of Philosophy, Department of Logic (short CV). My ORCID: orcid.org/0000000308340053
Grants

Principal Investigator: Czech Science Foundation (GACR), The role of set theory in modern mathematics, 2412141S. (20242026)

Principal Investigator: Mobility/Aktion Grant Czech Republic (FFUK, Department of Logic)  Austria, Vienna
(Department of Mathematics, V. Fischer), Compactness and cardinal invariants, 8J23AT015. (20232024)
 Principal investigator (with V. Fischer for FWF): Joint LeadAgency research grant between Austrian Science Foundation (FWF) and Czech Science Foundation (GACR), Compactness principles and combinatorics, 1929633L. (20192021)
 Principal Investigator: Mobility/Aktion Grant Czech Republic (FFUK, Department of Logic)  Austria, Vienna
(KGRC), Compactness and Cantor space, 8J19AT033. (20192020)
 Principal investigator (with Sy Friedman for FWF): Joint LeadAgency research grant between Austrian Science Foundation (FWF) and Czech Science Foundation (GACR), no I 1921N25, The continuum, forcing, and large cardinals. (20152017)
 Postdoc at Kurt Goedel Research Center, Vienna. (20132015)
 Principal Investigator: Mobility/Aktion Grant Czech Republic (FFUK, Department of Logic)  Austria, Vienna
(KGRC), Definability and Ideals, MEB061106. (20102012)
 Principal investigator: Postdoctoral grant by Czech Science Foundation (GACR), no. 201/09/P115. (20082011)
Preprints (research)

Generalized cardinal invariants for an inaccessible kappa with compactness at kappa++ (with S. Stejskalova), submitted (2023) [pdf]

Indestructibility of some compactness principles over models of PFA (with C. LambieHanson and S. Stejskalova), Annals of Pure and Applied Logic, 175(1,A), article no. 103359, 2024 [pdf]

Capturing sets of ordinals by normal ultrapowers (with M. Habic), Annals of Pure and Applied Logic, 174, article no. 103261, 2023 [pdf]

Small u(kappa) at singular kappa with compactness at kappa++ (with S. Stejskalova), Archive for Mathematical Logic, 61, 3354, 2022 [pdf]

Indestructibility of the tree property (with S. Stejskalova), The Journal of Symbolic Logic, 85(1), 467485, 2020 [pdf]

A Laverlike indestructibility for hypermeasurable cardinals, Archive for Mathematical Logic, 58(3), 275287, 2019 [pdf]

The tree property at aleph_{omega+2} with a finite gap (with Sy D. Friedman and S. Stejskalova), Fundamenta Mathematicae, 251, 219244, 2020 [pdf]

The Hyperuniverse Project and Maximality, Antos, C., Friedman, S.D., Honzik, R., Ternullo, C., Birkhauser Basel (Springer), 2018.

The tree property and the continuum function below aleph_omega (with S. Stejskalova), Mathematical Logic Quarterly, 64(12), 89102, 2018 [pdf]
 The tree property at the double successor of a singular cardinal with a larger gap (with Sy D. Friedman and S. Stejskalova), Annals of Pure and Applied Logic, 169, pp 548564, 2018 [pdf]
 A survey of special Aronszajn trees (with S. Stejskalova), Miscellanea Logica (X), Acta Univ. Car., Philosophica et Historica 1/2015, pp 7391, 2015 [pdf]
 Definability of satisfaction in outer models (with Sy D. Friedman), The Journal of Symbolic Logic, 81(3), pp 10471068, 2016 [pdf]
 The tree property at the aleph_{2n}'s and the failure of SCH at aleph_omega (with Sy D. Friedman), Annals of Pure and Applied Logic, 166, pp 526552, 2015 [pdf]
 Easton functions and supercompactness (with B.Cody and Sy D. Friedman), Fundamenta Mathematicae, 226, pp 279296, 2014 [pdf]
 On strong forms of reflection in set theory (with Sy D. Friedman), Mathematical Logic Quarterly, 62(12), pp 5258, 2016 [pdf]
 Multiverse conceptions in set theory (with C. Antos, S. D. Friedman, C. Ternullo), Synthese, 192(8), pp. 24632488, 2015 [pdf]
 A lifting argument for the generalized Grigorieff forcing (with J. Verner), Notre Dame Journal of Formal Logic , 57(2), pp 221231, 2016 [pdf]
 Supercompactness and Failures of GCH (with Sy D. Friedman), Fundamenta Mathematicae, 219(1), pp 1536, 2012 [pdf]
 Fusion and large cardinal preservation (with Sy D. Friedman and L. Zdomskyy), Annals of Pure and Applied Logic , 164, pp 12471273, 2013 [pdf]
 Easton's theorem and large cardinals from the optimal hypothesis (with Sy D. Friedman), Annals of Pure and Applied Logic, 163(12), pp 17381747, 2012 [pdf]
 A definable failure of the Singular Cardinal Hypothesis (with Sy D.
Friedman), Israel Journal of Mathematics, 192(2), pp 719762, 2012 [pdf]
 A characterization of lifting generics for Sackslike forcings, Acta Universitatis Carolinae, Mathematica et Physica, 51, pp 4955, 2010
[pdf]
 Global singularization and the failure of SCH, Annals of Pure and Applied Logic,
161(7), pp 895915, 2010 [pdf]
 Easton's theorem and large cardinals (with Sy D. Friedman), Annals of Pure and
Applied Logic, 154(3), pp 191208, 2008 [pdf]
Preprints (surveys)

Some lifting arguments for large and small cardinals (survey), 2020 [pdf]
 Large cardinals and their effect on the continuum function on regular cardinals, Miscellanea Logica (X), Acta Univ. Car., Philosophica et Historica 1/2015, pp 5572, 2015 [pdf]
 Large cardinals and the Continuum Hypothesis, Miscellanea Logica (IX), Acta Univ. Car., Philosophica et Historica 2/2010 , pp 3552, 2013 [pdf]
 Quick guide to independence results in set theory, Miscellanea Logica (VII), pp 89131, published by Charles Univerisity (FFUK) 2008 [pdf]
Other publications
 Translation (joint with Veronika Douchova). William J. Cook, Po stopach obchodniho cestujiciho, Dokoran, 2012.
 Translation. In: Logika 20.stoleti: Mezi filosofii a matematikou (edited
by Jaroslav Peregrin), Michal Dummet: Filosoficky vyznam Goedelovy vety,
Filosofia 2006.
 Coeditor of The Logica 2006 Yearbook, Filosofia, 2007.
Contact
Department of Logic
Charles University,
Celetna 20, Praha 1,
116 42, Czech
Republic
email: radek.honzik at ff.cuni.cz