Author:
Hamkins Joel David,Linetsky David,Reitz Jonas
Abstract
AbstractA pointwise definable model is one in which every object is definable without parameters. In a model of set theory, this property strengthens V = HOD, but is not first-order expressible. Nevertheless, if ZFC is consistent, then there are continuum many pointwise definable models of ZFC. If there is a transitive model of ZFC, then there are continuum many pointwise definable transitive models of ZFC. What is more, every countable model of ZFC has a class forcing extension that is pointwise definable. Indeed, for the main contribution of this article, every countable model of Gödel-Bernays set theory has a pointwise definable extension, in which every set and class is first-order definable without parameters.
Publisher
Cambridge University Press (CUP)
Reference13 articles.
1. Counting models of set theory
2. Reitz Jonas , The Ground Axiom, Ph.D. thesis, The Graduate Center of the City University of New York, 09 2006.
3. Forcing and models of arithmetic;Simpson;Proceeding of the American Mathematical Society,1974
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