INFINITE COMBINATORICS PLAIN AND SIMPLE
| Autor: | Dániel T. Soukup, Lajos Soukup |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Logic
Continuum (topology) Computer science 010102 general mathematics 03E05 03C98 05C63 03E35 54A35 Mathematics - Logic 0102 computer and information sciences Mathematical proof 01 natural sciences Combinatorics Set (abstract data type) Philosophy Range (mathematics) 010201 computation theory & mathematics Simple (abstract algebra) FOS: Mathematics Mathematics - Combinatorics Countable set Graph (abstract data type) Combinatorics (math.CO) Set theory 0101 mathematics Logic (math.LO) |
| Zdroj: | The Journal of Symbolic Logic. 83:1247-1281 |
| ISSN: | 1943-5886 0022-4812 |
| Popis: | 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. Comment: 29 pages, small revisions, to appear in JSL |
| Databáze: | OpenAIRE |
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