R. Honzik

activity

20132026

most citedIndestructibility of the tree property

7 citations · 7 across the 9 of their papers we have counts for

collaborators

10 papers

math.LO2026

Forcing in bounded arithmetic and set theory: analogies and differences

Radek Honzik, Ondrej Ježil, Mykyta Narusevych

We provide a modern overview of several forcing methods in bounded arithmetic and compare them with forcing in set theory. We specifically discuss the countable forcing framework o…

math.LO2026

Rado's Conjecture and the random algebra

Radek Honzik

Rado's Conjecture (RC) is a compactness principle for a certain class of partial orders, namely trees $T$ of height $ω_{1}$ without cofinal branches, postulating that a partial order…

math.LO2026

Forcing with random variables in bounded arithmetics and set theory

Radek Honzik

We analyse the Boolean-valued random forcing $B_{M, Ω}$ in bounded arithmetics developed in Krajicek (Forcing with random variables and proof complexity, vol. 382, Cambridge Univers…

math.LO2025

Compactness for small cardinals in mathematics: principles, consequences, and limitations

Radek Honzik

We discuss some well-known compactness principles for uncountable structures of small regular sizes ( $ω_{n}$ for $2 \leq n < ω$ , $ℵ_{ω + 1}$ , $ℵ_{ω^{2} + 1}$ , etc.), consistent from…

math.LO2023

Generalized cardinal invariants for an inaccessible $κ$ with compactness at $κ^{++}$

Radek Honzik, Sarka Stejskalova

We show that if the existence of a supercompact cardinal $κ$ with a weakly compact cardinal $λ$ above $κ$ is consistent, then the following are consistent as well (where $\mathfrak…

math.LO2022

Indestructibility of some compactness principles over models of PFA

Radek Honzik, Chris Lambie-Hanson, Šárka Stejskalová

We show that $PFA$ (Proper Forcing Axiom) implies that adding any number of Cohen subsets of $ω$ will not add an $ω_{2}$ -Aronszajn tree or a weak $ω_{1}$ -Kurepa tree, and more…

math.LO2019

Small u(kappa) at singular kappa with compactness at kappa++

Radek Honzik, Sarka Stejskalova

We show that the tree property, stationary reflection and the failure of approachability at $κ^{++}$ are consistent with $u (κ) = κ^{+} < 2^{κ}$ , where $κ$ is a singular stro…

math.LO2019★ 7 cited

Indestructibility of the tree property

Radek Honzik, Sarka Stejskalova

In the first part of the paper, we show that if $ω \leq κ < λ$ are cardinals, $κ^{< κ} = κ$ , and $λ$ is weakly compact, then in $V[\M(κ,λ)]$ the tree property at $λ= κ^{++V[\M(κ,λ)]}$…

math.LO2019

Capturing sets of ordinals by normal ultrapowers

Miha E. Habič, Radek Honzík

We investigate the extent to which ultrapowers by normal measures on $κ$ can be correct about powersets $P (λ)$ for $λ > κ$ . We consider two versions of this questions, the…

math.LO2013

Easton functions and supercompactness

Brent Cody, Sy-David Friedman, Radek Honzik

Suppose $κ$ is $λ$ -supercompact witnessed by an elementary embedding $j : V \to M$ with critical point $κ$ , and further suppose that $F$ is a function from the class of regula…

Forcing in bounded arithmetic and set theory: analogies and differences

Rado's Conjecture and the random algebra

Forcing with random variables in bounded arithmetics and set theory

Compactness for small cardinals in mathematics: principles, consequences, and limitations

Generalized cardinal invariants for an inaccessible κ with compactness at κ++

Indestructibility of some compactness principles over models of PFA

Small u(kappa) at singular kappa with compactness at kappa++

Indestructibility of the tree property

Capturing sets of ordinals by normal ultrapowers

Easton functions and supercompactness

Generalized cardinal invariants for an inaccessible $κ$ with compactness at $κ^{++}$