On equivalence relations Sigma_1^1-definable over H(kappa)
| dc.creator | Shelah, Saharon | |
| dc.creator | Väisänen, Pauli | |
| dc.date | 1999-11-29 | |
| dc.date.accessioned | 2026-07-07T05:32:00Z | |
| dc.date.available | 2026-07-07T05:32:00Z | |
| dc.description | Let kappa be an uncountable regular cardinal. Call an equivalence relation on functions from kappa into 2 Sigma_1^1-definable over H(kappa) if there is a first order sentence F and a parameter R subseteq H(kappa) such that functions f,g:kappa --> 2 are equivalent iff for some h:kappa --> 2, the structure (H(kappa),in,R,f,g,h) satisfies F, where in, R, f, g, and h are interpretations of the symbols appearing in F. All the values mu, 1 leq mu leq kappa^+ or mu=2^kappa, are possible numbers of equivalence classes for such a Sigma_1^1-equivalence relation. Additionally, the possibilities are closed under unions of <=kappa-many cardinals and products of <kappa-many cardinals. We prove that, consistent wise, these are the only restrictions under the singular cardinal hypothesis. The result is that the possible numbers of equivalence classes of Sigma_1^1-equivalence relations might consistent wise be exactly those cardinals which are in a prearranged set, provided that the singular cardinal hypothesis holds and that some necessary conditions are fulfilled. | |
| dc.identifier | https://arxiv.org/abs/math/9911231 | |
| dc.identifier | http://arxiv.org/abs/math/9911231 | |
| dc.identifier | Fund. Math. 174 No. 1 (2002) 1--21 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79503 | |
| dc.subject | Logic | |
| dc.subject | 03C55 (Primary) 03E35, 03C75 (Secondary) | |
| dc.title | On equivalence relations Sigma_1^1-definable over H(kappa) | |
| dc.type | text |