**RADEK HONZIK**

An assistant professor at the Charles University, Faculty of Philosophy, Department of Logic.

Lecture notes for courses I teach at the department of Logic can be downloaded here (you need to know the password; write to me if you do not know it).

**Grants**

- Postdoctoral grant by Czech Science Foundation (GACR), no. 201/09/P115. (2008-2011)
- Coordinator: Mobility Grant Czech Republic (FFUK, department of logic) - Austria, Vienna (KGRC) MEB061106. (2010-2012)
- Postdoc at Kurt Goedel Research Center, Vienna. (2013-2015)
- Project leader: 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)

**Preprints (research)**

- Easton's theorem and large cardinals (with Sy D. Friedman),
*Annals of Pure and Applied Logic*, 154(3), pp 191-208, 2008 [pdf] - Global singularization and the failure of SCH,
*Annals of Pure and Applied Logic,*161(7), pp 895-915, 2010 [pdf] - A characterization of lifting generics for Sacks-like forcings,
*Acta Universitatis Carolinae, Mathematica et Physica*, 51, pp 49-55, 2010 [pdf] - A definable failure of the Singular Cardinal Hypothesis (with Sy D.
Friedman),
*Israel Journal of Mathematics*, 192(2), pp 719-762, 2012 [pdf] - 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] - Fusion and large cardinal preservation (with Sy D. Friedman and L. Zdomskyy),
*Annals of Pure and Applied Logic*, 164, pp 1247-1273, 2013 [pdf] - Supercompactness and Failures of GCH (with Sy D. Friedman),
*Fundamenta Mathematicae*, 219(1), pp 15-36, 2012 [pdf] - A lifting argument for the generalized Grigorieff forcing (with J. Verner),
*Notre Dame Journal of Formal Logic*, 57(2), pp 221-231, 2016 [pdf] - Multiverse conceptions in set theory (with C. Antos, S. D. Friedman, C. Ternullo),
*Synthese*, 192(8), pp. 2463-2488, 2015 [pdf] - On strong forms of reflection in set theory (with Sy D. Friedman),
*Mathematical Logic Quarterly*, 62(1-2), pp 52-58, 2016 [pdf] - Easton functions and supercompactness (with B.Cody and Sy D. Friedman),
*Fundamenta Mathematicae*, 226, pp 279-296, 2014 [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 526-552, 2015 [pdf] - Definability of satisfaction in outer models (with Sy D. Friedman),
*Journal of Symbolic Logic*, 81(3), pp 1047-1068, 2016 [pdf] - 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] - The tree property at the double successor of a singular cardinal with a larger gap (with Sy D. Friedman and S. Stejskalova), submitted [pdf]
- The tree property and the continuum function below aleph_omega (with S. Stejskalova), submitted [pdf]
- Preserving measurability with Cohen iterations, to appear in
*Miscellanea Logica, Acta Univ. Car., Philosophica et Historica*[pdf] - The tree property at aleph_{\omega+2} with a finite gap (with Sy D. Friedman and S. Stejskalova), submitted [pdf]

**Preprints (surveys)**

- Quick guide to independence results in set theory,
*Miscellanea Logica (VII)*, pp 89-131, published by Charles Univerisity (FFUK) 2008 [pdf] - Large cardinals and the Continuum Hypothesis,
*Miscellanea Logica (IX), Acta Univ. Car., Philosophica et Historica 2/2010*, pp 35-52, 2013 [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 55-72, 2015 [pdf]

**Other**

- Co-editor of The Logica 2006 Yearbook, Filosofia, 2007.
- Translation. In: Logika 20.stoleti: Mezi filosofii a matematikou (edited by Jaroslav Peregrin), Michal Dummet: Filosoficky vyznam Goedelovy vety, Filosofia 2006.
- Translation (joint with Veronika Douchova). William J. Cook,
*Po stopach obchodniho cestujiciho,*Dokoran, 2012.

**Contact**

Department of Logic

Charles University,

Celetna 20, Praha 1,

116 42, Czech
Republic

email: radek.honzik at ff.cuni.cz