Pointwise definable models of set theory
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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.
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1987 ◽
Vol 30
(4)
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pp. 385-392
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1976 ◽
Vol 41
(1)
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pp. 139-145
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2013 ◽
Vol 13
(02)
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pp. 1350006
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