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  1.  48
    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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  2.  15
    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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  3.  72
    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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  4.  8
    Inner mantles and iterated HOD.Jonas Reitz & Kameryn J. Williams - 2019 - Mathematical Logic Quarterly 65 (4):498-510.
    We present a class forcing notion, uniformly definable for ordinals η, which forces the ground model to be the ηth inner mantle of the extension, in which the sequence of inner mantles has length at least η. This answers a conjecture of Fuchs, Hamkins, and Reitz [1] in the positive. We also show that forces the ground model to be the ηth iterated of the extension, where the sequence of iterated s has length at least η. We conclude by showing (...)
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  5. Inner-Model Reflection Principles.Neil Barton, Andrés Eduardo Caicedo, Gunter Fuchs, Joel David Hamkins, Jonas Reitz & Ralf Schindler - 2020 - Studia Logica 108 (3):573-595.
    We introduce and consider the inner-model reflection principle, which asserts that whenever a statement \varphi(a) 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 W \subset A. A stronger principle, the ground-model reflection principle, asserts that any such \varphi(a) 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 (...)
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    Cohen forcing and inner models.Jonas Reitz - 2020 - Mathematical Logic Quarterly 66 (1):65-72.
    Given an inner model and a regular cardinal κ, we consider two alternatives for adding a subset to κ by forcing: the Cohen poset Add(κ, 1), and the Cohen poset of the inner model. The forcing from W will be at least as strong as the forcing from V (in the sense that forcing with the former adds a generic for the latter) if and only if the two posets have the same cardinality. On the other hand, a sufficient condition (...)
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