scholarly journals Elementary submodels in infinite combinatorics

2011 ◽  
Vol 311 (15) ◽  
pp. 1585-1598 ◽  
Author(s):  
Lajos Soukup
Keyword(s):  
Elementary Submodels ◽  
Infinite Combinatorics

scholarly journals INFINITE COMBINATORICS PLAIN AND SIMPLE

2018 ◽  
Vol 83 (3) ◽  
pp. 1247-1281 ◽  
Author(s):  
DÁNIEL T. SOUKUP ◽  
LAJOS SOUKUP
Keyword(s):  
Chromatic Number ◽  
Set Theory ◽  
Wide Applicability ◽  
Elementary Submodels ◽  
Set Systems ◽  
Point Set ◽  
Infinite Combinatorics ◽  
Sparse Set ◽  
Paradoxical Decompositions ◽  
General Method

AbstractWe 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.

Infinite Combinatorics and Graphs

2000 ◽  
pp. 161-210
Author(s):  
John M. Harris ◽  
Jeffry L. Hirst ◽  
Michael J. Mossinghoff
Keyword(s):  
Infinite Combinatorics

Infinite Combinatorics and Graphs

2008 ◽  
pp. 281-353
Author(s):  
John M. Harris ◽  
Jeffry L. Hirst ◽  
Michael J. Mossinghoff
Keyword(s):  
Infinite Combinatorics

scholarly journals The topology of elementary submodels

1998 ◽  
Vol 82 (1-3) ◽  
pp. 239-266 ◽  
Author(s):  
Lúcia R. Junqueira ◽  
Franklin D. Tall
Keyword(s):  
Elementary Submodels
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