Elementary extensions of countable models of set theory

12 March 1976

journal article
Published by Cambridge University Press (CUP) in The Journal of Symbolic Logic

Vol. 41 (1) , 139-145
https://doi.org/10.2307/2272952

Abstract

We prove the following extension of a result of Keisler and Morley. Suppose is a countable model of ZFC and c is an uncountable regular cardinal in . Then there exists an elementary extension of 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.

Keywords

COUNTABLE MODELS
UNCOUNTABLE
KEISLER
ENLARGES
ORDINALS
SUPPOSE
ZFC
CARDINAL

This publication has 3 references indexed in Scilit:

Elementary extensions of models of set theory
Israel Journal of Mathematics, 1968
Partitions and models
Published by Springer Nature ,1968
A minimal model for set theory
Bulletin of the American Mathematical Society, 1963