On the non-existence of mad families
| Autor: | Saharon Shelah, Haim Horowitz |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Logic
Existential quantification 010102 general mathematics Mathematics::General Topology 0102 computer and information sciences 01 natural sciences Graph Combinatorics Mathematics::Logic Philosophy 010201 computation theory & mathematics Inaccessible cardinal Maximal independent set 0101 mathematics Mathematics |
| Zdroj: | Archive for Mathematical Logic. 58:325-338 |
| ISSN: | 1432-0665 0933-5846 |
| DOI: | 10.1007/s00153-018-0640-5 |
| Popis: | We show that the non-existence of mad families is equiconsistent with $$\textit{ZFC}$$ , answering an old question of Mathias. We also consider the above result in the general context of maximal independent sets in Borel graphs, and we construct a Borel graph G such that $$\textit{ZF}+\textit{DC}+$$ “there is no maximal independent set in G” is equiconsistent with $$\textit{ZFC}+$$ “there exists an inaccessible cardinal”. |
| Databáze: | OpenAIRE |
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