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Article #125combinatorial set theory
From: Claudio Gutierrez
Date: Wed, 11 Nov 1992 16:40
Date: Wed, 11 Nov 1992 16:40
16 lines
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1186 bytes
Keywords:
I need the following result (that can be of comon sense)
Exists a family of sets *A* = { Ai}_{i \in \omega}
such that there is a family
*F* of infinite subsets of *A* with |*F*|=2^{\omega}
with the properties:
i) Each B \in *F* has F.I.P. (The intersection of a
finite numbers of elements of each B \in *F* is non empty.
ii) For all B \in *F* , the intersection of all the
elements of B is empty.
iii) For all B={B1,B2,...} \in *F*, B'={B'12,B'2,...} \in *F*
there exists n \in |N such that
Intersection{B1,...,Bn} and Intersection{B'1,..,B'n}
are dosjoint.
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<1992Nov11.164014.14768@tolten.puc.cl>Path:
arc1-ca.pugleaf.net!sparky!uunet!sun-barr!cs.utexas.edu!usc!zaphod.mps.ohio-state.edu!uwm.edu!ux1.cso.uiuc.edu!news.cso.uiuc.edu!usenetShow Full Headers
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Newsgroups: sci.math.research Path: arc1-ca.pugleaf.net!sparky!uunet!sun-barr!cs.utexas.edu!usc!zaphod.mps.ohio-state.edu!uwm.edu!ux1.cso.uiuc.edu!news.cso.uiuc.edu!usenet From: cgutierr@mat.puc.cl (Claudio Gutierrez) Subject: combinatorial set theory Message-ID: <1992Nov11.164014.14768@tolten.puc.cl> Sender: Daniel Grayson <dan@math.uiuc.edu> X-Submissions-To: sci-math-research@uiuc.edu Organization: Pontificia Universidad Catolica de Chile X-Administrivia-To: sci-math-research-request@uiuc.edu Approved: Daniel Grayson <dan@math.uiuc.edu> Date: Wed, 11 Nov 1992 16:40:14 GMT Lines: 17