A model in which the Separation principle holds for a given effective projective Sigma-class
| Autor: | Kanovei, Vladimir, Lyubetsky, Vassily |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Axioms 2022, 11, no. 3, article no. 122 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.3390/axioms11030122 |
| Popis: | In this paper, we prove the following: If $n\ge3$, there is a generic extension of $L$ -- the constructible universe -- in which it is true that the Separation principle holds for both effective (lightface) classes $\varSigma^1_n$ and $\varPi^1_n$ for sets of integers. The result was announced long ago by Leo Harrington with a sketch of the proof for $n=3$; its full proof has never been presented. Our methods are based on a countable product of almost-disjoint forcing notions independent in the sense of Jensen--Solovay. Comment: 17 pages |
| Databáze: | arXiv |
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