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Determinacy and the sharp function on objects of type k
Published online by Cambridge University Press: 12 March 2014
Abstract
We characterize, in terms of determinacy, the existence of the least inner model of “every object of type k has a sharp.” For k ∈ ω, we define two classes of sets, and , which lie strictly between and . Let #k be the (partial) sharp function on objects of type k. We show that the determinacy of follows from
L[#k] ⊨ “every object of type k has a sharp”,
and we show that the existence of indiscemibles for L[#k] is equivalent to a slightly stronger determinacy hypothesis, the determinacy of .
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- Research Article
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- Copyright © Association for Symbolic Logic 1995
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