The power set of $\omega $ Elementary submodels and weakenings of CH
Tom 170 / 2001
Fundamenta Mathematicae 170 (2001), 257-265
MSC: Primary 03E50, 03E35.
DOI: 10.4064/fm170-3-4
Streszczenie
We define a new principle, $\mathop {\rm SEP}\nolimits $, which is true in all Cohen extensions of models of $\mathop {\rm CH}\nolimits $, and explore the relationship between $\mathop {\rm SEP}\nolimits $ and other such principles. $\mathop {\rm SEP}\nolimits $ is implied by each of $\mathop {\rm CH}\nolimits ^*$, the weak Freeze–Nation property of ${\cal P}(\omega )$, and the $(\aleph _1,\aleph _0)$-ideal property. $\mathop {\rm SEP}\nolimits $ implies the principle ${\rm C}_2^{\rm s}(\omega _2)$, but does not follow from ${\rm C}_2^{\rm s}(\omega _2)$, or even ${\rm C}^{\rm s}(\omega _2)$.
