Elementary extensions of countable models of set theory

Journal of Symbolic Logic 41 (1):139-145 (1976)
We prove the following extension of a result of Keisler and Morley. Suppose U is a countable model of ZFC and c is an uncountable regular cardinal in U. Then there exists an elementary extension of U which fixes all ordinals below c, enlarges c, and either (i) contains or (ii) does not contain a least new ordinal. Related results are discussed.
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DOI 10.2307/2272952
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