Geodesic
The power set of $\omega $ Elementary submodels and weakenings of CH
István Juhász 1   ; Kenneth Kunen 2
1 Alfréd Rényi Institute of Mathematics Hungarian Academy of Sciences P.O. Box 127 H-1364 Budapest, Hungary
2 Department of Mathematics University of Wisconsin Madison, WI 53706, U.S.A.
Fundamenta Mathematicae, Tome 170 (2001) no. 3, pp. 257-265 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 ${\rm C}^{\rm s}(\omega _2)$.
DOI : 10.4064/fm170-3-4
Keywords: define principle mathop sep nolimits which cohen extensions models mathop nolimits explore relationship between mathop sep nolimits other principles mathop sep nolimits implied each mathop nolimits * weak freeze nation property cal omega aleph aleph ideal property mathop sep nolimits implies principle omega does follow omega even omega

István Juhász  1   ; Kenneth Kunen  2

1 Alfréd Rényi Institute of Mathematics Hungarian Academy of Sciences P.O. Box 127 H-1364 Budapest, Hungary
2 Department of Mathematics University of Wisconsin Madison, WI 53706, U.S.A. 
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Elementary submodels and weakenings of CH
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István Juhász; Kenneth Kunen. The power set of $\omega $
Elementary submodels and weakenings of CH. Fundamenta Mathematicae, Tome 170 (2001) no. 3, pp. 257-265. doi: 10.4064/fm170-3-4

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