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Characterising subsets of ω1 constructible from a real

Published online by Cambridge University Press:  12 March 2014

P. D. Welch
P. D. Welch*
Affiliation:
Department of Mathematics, UCLA, Los Angeles, California 90024, E-mail: welch@math.ucla.edu
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Abstract

A small large cardinal upper bound in V for proving when certain subsets of ω1 (including the universally Baire subsets) are precisely those constructible from a real is given. In the core model we find an exact equivalence in terms of the length of the mouse order; we show that ∀B ⊆ ω1 [B is universally Baire ⇔ B ϵ L[r] for some real r] is preserved under set-sized forcing extensions if and only if there are arbitrarily large “admissibly measurable” cardinals.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 59 , Issue 4 , December 1994 , pp. 1420 - 1432
Copyright
Copyright © Association for Symbolic Logic 1994

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References

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