6 papers · 1 filter
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 of height without cofinal branches, postulating that a partial order…
Forcing with random variables in bounded arithmetics and set theory
Radek Honzik
We analyse the Boolean-valued random forcing in bounded arithmetics developed in Krajicek (Forcing with random variables and proof complexity, vol. 382, Cambridge Univers…
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 ( for , , , etc.), consistent from…
Generalized cardinal invariants for an inaccessible with compactness at
Radek Honzik, Sarka Stejskalova
We show that if the existence of a supercompact cardinal with a weakly compact cardinal above is consistent, then the following are consistent as well (where $\mathfrak…
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 are consistent with , where is a singular stro…
Indestructibility of the tree property
Radek Honzik, Sarka Stejskalova
In the first part of the paper, we show that if are cardinals, , and is weakly compact, then in $V[\M(κ,λ)]$ the tree property at $λ= κ^{++V[\M(κ,λ)]}$…