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Chains of end elementary extensions of models of set theory

Published online by Cambridge University Press:  12 March 2014

Andrés Villaveces
Andrés Villaveces*
Affiliation:
Mathematics Institute, Hebrew University, 91904 Jerusalem, Israel Departamento de Matematicas, Universidad Nacional, Bogota, Columbia E-mail: villavec@matematicas.unal.edu.co
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Abstract

Large cardinals arising from the existence of arbitrarily long end elementary extension chains over models of set theory are studied here. In particular, we show that the large cardinals obtained in this fashion (‘unfoldable cardinals’) lie in the boundary of the propositions consistent with ‘V = L’ and the existence of 0#. We also provide an ‘embedding characterisation’ of the unfoldable cardinals and study their preservation and destruction by various forcing constructions.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 3 , September 1998 , pp. 1116 - 1136
Copyright
Copyright © Association for Symbolic Logic 1998

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