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The cardinal characteristic for relative gamma-sets | | Arnold W. Miller
; | | Date: |
25 May 2004 | | Subject: | Logic; General Topology MSC-class: 03E35 54D20 03E50 | math.LO math.GN | | Abstract: | For $X$ a separable metric space define $pp(X)$ to be the smallest cardinality of a subset $Z$ of $X$ which is not a relative $ga$-set in $X$, i.e., there exists an $om$-cover of $X$ with no $ga$-subcover of $Z$. We give a characterization of $pp(2^om)$ and $pp(om^om)$ in terms of definable free filters on $om$ which is related to the psuedointersection number $pp$. We show that for every uncountable standard analytic space $X$ that either $pp(X)=pp(2^om)$ or $pp(X)=pp(om^om)$. We show that both of following statements are each relatively consistent with ZFC: (a) $pp=pp(om^om) < pp(2^om)$ and (b) $pp < pp(om^om) =pp(2^om)$ | | Source: | arXiv, math.LO/0405473 | | Services: | Forum | Review | PDF | Favorites | |
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