R. Honzik

collaborators

4 papers

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 $I ¨ _{1}$ without cofinal branches, postulating that a partial orde…

math.LO2026

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 ( $I ¨ _{n}$ for $2 \leq n < I ¨ $ , $ℵ_{I ¨ + 1}$ , $ℵ_{I ¨ ^{2} + 1}$ , etc.), consistent…

math.LO2026

Forcing with random variables in bounded arithmetics and set theory

Radek Honzik

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

math.LO2025

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

Radek Honzik, Sarka Stejskalova

We show that if the existence of a supercompact cardinal $I^º$ with a weakly compact cardinal $I^»$ above $I^º$ is consistent, then the following are consistent as well (where $\mathf…

Rado's Conjecture and the random algebra

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

Forcing with random variables in bounded arithmetics and set theory

Generalized cardinal invariants for an inaccessible I^º with compactness at I^º++

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