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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Representing sets of ordinals as countable unions of sets in the core model


Author: Menachem Magidor
Journal: Trans. Amer. Math. Soc. 317 (1990), 91-126
MSC: Primary 03E45; Secondary 03E35
DOI: https://doi.org/10.1090/S0002-9947-1990-0939805-5
MathSciNet review: 939805
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Abstract: We prove the following theorems.

Theorem 1 $ (\neg {0^\char93 })$. Every set of ordinals which is closed under primitive recursive set functions is a countable union of sets in $ L$.

Theorem 2. (No inner model with an Erdàs cardinal, i.e. $ \kappa \to {({\omega _1})^{ < \omega }}$.) For every ordinal $ \beta $, there is in $ K$ an algebra on $ \beta $ with countably many operations such that every subset of $ \beta $ closed under the operations of the algebra is a countable union of sets in $ K$.


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DOI: https://doi.org/10.1090/S0002-9947-1990-0939805-5
Article copyright: © Copyright 1990 American Mathematical Society