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Locally countable models of Σ1-separation
Published online by Cambridge University Press: 12 March 2014
Abstract
Let α be any countable admissible ordinal greater than ω. There is a transitive set A such that A is admissible, locally countable, OnA = α, and A satisfies Σ1-separation. In fact, if B is any nonstandard model of KP + ∀x ⊆ ω (the hyperjump of x exists), the ordinal standard part of B is greater than ω, and every standard ordinal in B is countable in B, then HCB ∩ (standard part of B) satisfies Σ-separation.
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- Copyright © Association for Symbolic Logic 1981
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