A property equivalent to the existence of scales
Author:
Howard Becker
Journal:
Trans. Amer. Math. Soc. 287 (1985), 591-612
MSC:
Primary 03E60; Secondary 03E15
DOI:
https://doi.org/10.1090/S0002-9947-1985-0768727-6
MathSciNet review:
768727
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Abstract | References | Similar Articles | Additional Information
Abstract: Let and
be the propositions that every relation on
can be uniformized, and every subset of
admits a scale, respectively. For
, let
denote the Wadge ordinal of
, and let
be the supremum of the ordinals realized in the pointclass
.
Theorem . The following are equivalent:
(a) ,
(b) the set
contains an
-cub subset of
.
Using this theorem, Woodin has shown that if the theory is consistent, then the theory
is also consistent. In this paper we give a proof of the above theorem and of a local version of it. We also study the ordinal
and give several characterizations of it.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1985-0768727-6
Article copyright:
© Copyright 1985
American Mathematical Society