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Heights of models of ZFC and the existence of end elementary extensions II

Published online by Cambridge University Press:  12 March 2014

Andrés Villaveces
Andrés Villaveces*
Affiliation:
Department of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel Dpto. de Matemáticas, Univ. Nacional de Colombia, Santa Fe De Bogotá, Colombia E-mail: villavec@math.huji.ac.il
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Abstract

The existence of End Elementary Extensions of modelsM of ZFC is related to the ordinal height of M, according to classical results due to Keisler, Morley and Silver. In this paper, we further investigate the connection between the height of M and the existence of End Elementary Extensions of M. In particular, we prove that the theory ‘ZFC + GCH + there exist measurable cardinals + all inaccessible non weakly compact cardinals are possible heights of models with no End Elementary Extensions’ is consistent relative to the theory ‘ZFC + GCH + there exist measurable cardinals + the weakly compact cardinals are cofinal in ON’. We also provide a simpler coding that destroys GCH but otherwise yields the same result.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 3 , September 1999 , pp. 1111 - 1124
Copyright
Copyright © Association for Symbolic Logic 1999

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References

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