Doc. Radek Honzik, Ph.D.

Professor at Charles University,  Faculty of Philosophy, Department of Logic (short CV). My ORCID: orcid.org/0000-0003-0834-0053

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)

Preprints (research)

1. Generalized cardinal invariants for an inaccessible kappa with compactness at kappa++ (with S. Stejskalova), submitted (2023) [pdf]
2. Indestructibility of some compactness principles over models of PFA (with C. Lambie-Hanson and S. Stejskalova), Annals of Pure and Applied Logic, 175(1,A), article no. 103359, 2024 [pdf]
3. Capturing sets of ordinals by normal ultrapowers (with M. Habic), Annals of Pure and Applied Logic, 174, article no. 103261, 2023 [pdf]
4. Small u(kappa) at singular kappa with compactness at kappa++ (with S. Stejskalova), Archive for Mathematical Logic, 61, 33-54, 2022 [pdf]
5. Indestructibility of the tree property (with S. Stejskalova), The Journal of Symbolic Logic, 85(1), 467-485, 2020 [pdf]
6. A Laver-like indestructibility for hypermeasurable cardinals, Archive for Mathematical Logic, 58(3), 275-287, 2019 [pdf]
7. The tree property at aleph_{omega+2} with a finite gap (with Sy D. Friedman and S. Stejskalova), Fundamenta Mathematicae, 251, 219-244, 2020 [pdf]
8. The Hyperuniverse Project and Maximality, Antos, C., Friedman, S.-D., Honzik, R., Ternullo, C., Birkhauser Basel (Springer), 2018.
9. The tree property and the continuum function below aleph_omega (with S. Stejskalova), Mathematical Logic Quarterly, 64(1-2), 89-102, 2018 [pdf]
10. 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 548-564, 2018 [pdf]
11. A survey of special Aronszajn trees (with S. Stejskalova), Miscellanea Logica (X), Acta Univ. Car., Philosophica et Historica 1/2015, pp 73-91, 2015 [pdf]
12. Definability of satisfaction in outer models (with Sy D. Friedman), The Journal of Symbolic Logic, 81(3), pp 1047-1068, 2016 [pdf]
13. 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 526-552, 2015 [pdf]
14. Easton functions and supercompactness (with B.Cody and Sy D. Friedman), Fundamenta Mathematicae, 226, pp 279-296, 2014 [pdf]
15. On strong forms of reflection in set theory (with Sy D. Friedman), Mathematical Logic Quarterly, 62(1-2), pp 52-58, 2016 [pdf]
16. Multiverse conceptions in set theory (with C. Antos, S. D. Friedman, C. Ternullo), Synthese, 192(8), pp. 2463-2488, 2015 [pdf]
17. A lifting argument for the generalized Grigorieff forcing (with J. Verner), Notre Dame Journal of Formal Logic , 57(2), pp 221-231, 2016 [pdf]
18. Supercompactness and Failures of GCH (with Sy D. Friedman), Fundamenta Mathematicae, 219(1), pp 15-36, 2012 [pdf]
19. Fusion and large cardinal preservation (with Sy D. Friedman and L. Zdomskyy), Annals of Pure and Applied Logic , 164, pp 1247-1273, 2013 [pdf]
20. Easton's theorem and large cardinals from the optimal hypothesis (with Sy D. Friedman), Annals of Pure and Applied Logic, 163(12), pp 1738-1747, 2012 [pdf]
21. A definable failure of the Singular Cardinal Hypothesis (with Sy D. Friedman), Israel Journal of Mathematics, 192(2), pp 719-762, 2012 [pdf]
22. A characterization of lifting generics for Sacks-like forcings, Acta Universitatis Carolinae, Mathematica et Physica, 51, pp 49-55, 2010 [pdf]
23. Global singularization and the failure of SCH,  Annals of Pure and Applied Logic, 161(7), pp 895-915, 2010  [pdf]
24. Easton's theorem and large cardinals (with Sy D. Friedman),  Annals of Pure and Applied Logic, 154(3), pp 191-208, 2008 [pdf]

Preprints (surveys)

1. Some lifting arguments for large and small cardinals (survey), 2020 [pdf]
2. Large cardinals and their effect on the continuum function on regular cardinals, Miscellanea Logica (X), Acta Univ. Car., Philosophica et Historica 1/2015, pp 55-72, 2015 [pdf]
3. Large cardinals and the Continuum Hypothesis, Miscellanea Logica (IX), Acta Univ. Car., Philosophica et Historica 2/2010 , pp 35-52, 2013 [pdf]
4. Quick guide to independence results in set theory, Miscellanea Logica (VII), pp 89-131, published by Charles Univerisity (FFUK) 2008 [pdf]

Other publications

1. Translation (joint with Veronika Douchova). William J. Cook, Po stopach obchodniho cestujiciho, Dokoran, 2012.
2. Translation. In: Logika 20.stoleti: Mezi filosofii a matematikou (edited by Jaroslav Peregrin), Michal Dummet: Filosoficky vyznam Goedelovy vety, Filosofia 2006.
3. Co-editor 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