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Determinacy and the sharp function on objects of type k

Published online by Cambridge University Press:  12 March 2014

Derrick Albert Dubose
Derrick Albert Dubose*
Affiliation:
Department of Mathematics, University of Nevada, Las Vegas, Nevada 89154, E-mail: dubose@nevada.edu
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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 .

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 60 , Issue 4 , December 1995 , pp. 1025 - 1053
Copyright
Copyright © Association for Symbolic Logic 1995

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References

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