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INFINITE COMBINATORICS PLAIN AND SIMPLE

Published online by Cambridge University Press:  23 October 2018

DÁNIEL T. SOUKUP  and
LAJOS SOUKUP
DÁNIEL T. SOUKUP
Affiliation:
KURT GÖDEL RESEARCH CENTER FOR MATHEMATICAL LOGIC UNIVERSITÄT WIEN, WIEN, AUSTRIAE-mail: daniel.soukup@univie.ac.atURL: http://www.logic.univie.ac.at/∼soukupd73/
LAJOS SOUKUP
Affiliation:
HUNGARIAN ACADEMY OF SCIENCES ALFRÉD RÉNYI INSTITUTE OF MATHEMATICS, BUDAPEST, HUNGARYE-mail: soukup@renyi.huURL: http://www.renyi.hu/∼soukup
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Abstract

We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already, we significantly broaden this framework by developing the corresponding technique for countably closed models of size continuum. The applications range from various theorems on paradoxical decompositions of the plane, to coloring sparse set systems, results on graph chromatic number and constructions from point-set topology. Our main purpose is to demonstrate the ease and wide applicability of this method in a form accessible to anyone with a basic background in set theory and logic.

Keywords

03E0503C9805C6303E3554A35elementary submodelsDavies-treecloudschromatic numberalmost disjointBernsteinCantorcoloringsplendidcountably closed
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 3 , September 2018 , pp. 1247 - 1281
Copyright
Copyright © The Association for Symbolic Logic 2018 

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