On equivalence relations Sigma_1^1-definable over H(kappa)

Details On equivalence relations Sigma_1^1-definable over H(kappa) On equivalence relations Sigma_1^1-definable over H(kappa)

1999-11-29

arxiv.org/abs/math/9911231v1

Mathematics

Logic

Scientific paper

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

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