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HENKIN CONSTRUCTIONS OF MODELS WITH SIZE CONTINUUM

Published online by Cambridge University Press:  01 April 2019

JOHN T. BALDWIN  and
MICHAEL C. LASKOWSKI
JOHN T. BALDWIN
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF ILLINOIS AT CHICAGO CHICAGO, IN 60607-7045, USA E-mail: jbaldwin@uic.edu
MICHAEL C. LASKOWSKI
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF MARYLAND COLLEGE PARK, MD 20742, USA E-mail: mcl@math.umd.edu
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Abstract

We describe techniques for constructing models of size continuum in ω steps by simultaneously building a perfect set of enmeshed countable Henkin sets. Such models have perfect, asymptotically similar subsets. We survey applications involving Borel models, atomic models, two-cardinal transfers and models respecting various closure relations.

Keywords

Primary 03C50Secondary 03C3003C25Henkin setsasymptotic similarityBorel modelatomic model
Type
Articles
Information
Bulletin of Symbolic Logic , Volume 25 , Issue 1 , March 2019 , pp. 1 - 33
Copyright
Copyright © The Association for Symbolic Logic 2019 

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