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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 of height 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 in bounded arithmetics developed in Krajicek (Forcing with random variables and proof complexity, vol. 382, Cambridge Univers…