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  1.  24
    Set-Theoretic Geology.Gunter Fuchs, Joel David Hamkins & Jonas Reitz - 2015 - Annals of Pure and Applied Logic 166 (4):464-501.
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    The Ground Axiom.Jonas Reitz - 2007 - Journal of Symbolic Logic 72 (4):1299 - 1317.
    A new axiom is proposed, the Ground Axiom, asserting that the universe is not a nontrivial set forcing extension of any inner model. The Ground Axiom is first-order expressible, and any model of ZFC has a class forcing extension which satisfies it. The Ground Axiom is independent of many well-known set-theoretic assertions including the Generalized Continuum Hypothesis, the assertion V=HOD that every set is ordinal definable, and the existence of measurable and supercompact cardinals. The related Bedrock Axiom, asserting that the (...)
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    Inner-Model Reflection Principles.Neil Barton, Andrés Eduardo Caicedo, Gunter Fuchs, Joel David Hamkins, Jonas Reitz & Ralf Schindler - forthcoming - Studia Logica:1-23.
    We introduce and consider the inner-model reflection principle, which asserts that whenever a statement \\) in the first-order language of set theory is true in the set-theoretic universe V, then it is also true in a proper inner model \. A stronger principle, the ground-model reflection principle, asserts that any such \\) true in V is also true in some non-trivial ground model of the universe with respect to set forcing. These principles each express a form of width reflection in (...)
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    Pointwise Definable Models of Set Theory.Joel David Hamkins, David Linetsky & Jonas Reitz - 2013 - Journal of Symbolic Logic 78 (1):139-156.
    A pointwise definable model is one in which every object is \loos 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. (...)
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