Definability and almost disjoint families
| Autor: | Asger Törnquist |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
General Mathematics
010102 general mathematics 03E05 03E15 03E35 03E45 03E50 Mathematics::General Topology Mathematics - Logic 0102 computer and information sciences Disjoint sets 01 natural sciences Combinatorics Mathematics::Logic 010201 computation theory & mathematics FOS: Mathematics 0101 mathematics Logic (math.LO) Axiom Mathematics |
| Popis: | We show that there are no infinite maximal almost disjoint ("mad") families in Solovay's model, thus solving a long-standing problem posed by A.D.R. Mathias in 1967. We also give a new proof of Mathias' theorem that no analytic infinite almost disjoint family can be maximal, and show more generally that if Martin's Axiom holds at $\kappa Comment: Changes in version 2: (1) The proof of Claim 2 on p. 9 has been fixed. (2) Notation regarding characteristic functions and the sets they define has been explained more clearly (3) Typos corrected throughout the manuscript |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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