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# Representing Sets of Ordinals as Countable Unions of Sets in the Core Model

Menachem Magidor
Transactions of the American Mathematical Society
Vol. 317, No. 1 (Jan., 1990), pp. 91-126
DOI: 10.2307/2001455
Stable URL: http://www.jstor.org/stable/2001455
Page Count: 36
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## Abstract

We prove the following theorems. Theorem 1 (|neg 0|tt#). 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 Erdos cardinal, i.e. $\kappa \rightarrow (\omega_1)^{<\omega}$.) For every ordinal β, there is in K an algebra on β with countably many operations such that every subset of β closed under the operations of the algebra is a countable union of sets in K.

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