Set theory with free construction principles
Some combinatorial principles defined in terms of elementary submodels
We give an equivalent, but simpler formulation of the axiom SEP, which was introduced in [9] in order to capture some of the combinatorial behaviour of models of set theory obtained by adding Cohen reals to a model of CH. Our formulation shows that many of the consequences of the weak Freese-Nation property of 𝒫(ω) studied in [6] already follow from SEP. We show that it is consistent that SEP holds while 𝒫(ω) fails to have the (ℵ₁,ℵ ₀)-ideal property introduced in [2]. This answers a question...
Some topological consequences of the Product Measure Extension Axiom
Strong Fubini axioms from measure extension axioms
It is shown that measure extension axioms imply various forms of the Fubini theorem for nonmeasurable sets and functions in Radon measure spaces.