INFINITE COMBINATORICS PLAIN AND SIMPLE

被引：5

作者：

Soukup, Daniel T. ^{[1
]}

Soukup, Lajos ^{[2
]}

机构：

[1] Univ Wien, Kurt Godel Res Ctr Math Log, Vienna, Austria

[2] Hungarian Acad Sci, Alfred Renyi Inst Math, Budapest, Hungary

来源：

JOURNAL OF SYMBOLIC LOGIC | 2018年 / 83卷 / 03期

基金：

奥地利科学基金会;

关键词：

elementary submodels; Davies-tree; clouds; chromatic number; almost disjoint; Bernstein; Cantor; coloring; splendid; countably closed; CONFLICT-FREE COLORINGS; ELEMENTARY SUBMODELS; CHROMATIC NUMBER; FAMILIES; CLOUDS; GRAPHS; COVER;

D O I：

10.1017/jsl.2018.8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 sub-models 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.

引用

页码：1247 / 1281

页数：35