A+ CATEGORY SCIENTIFIC UNIT

The power set of $\omega $ Elementary submodels and weakenings of CH

Volume 170 / 2001

István Juhász, Kenneth Kunen Fundamenta Mathematicae 170 (2001), 257-265 MSC: Primary 03E50, 03E35. DOI: 10.4064/fm170-3-4

Abstract

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 ${\rm C}^{\rm s}(\omega _2)$.

Authors

  • István JuhászAlfréd Rényi Institute of Mathematics
    Hungarian Academy of Sciences
    P.O. Box 127
    H-1364 Budapest, Hungary
    e-mail
  • Kenneth KunenDepartment of Mathematics
    University of Wisconsin
    Madison, WI 53706, U.S.A.
    e-mail

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