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  1. Ordinal definability in Jensen's model.Włodzimierz Zadrożny - 1984 - Journal of Symbolic Logic 49 (2):608-620.
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  • Iterating the Cofinality- Constructible Model.Ur Ya’Ar - 2023 - Journal of Symbolic Logic 88 (4):1682-1691.
    We investigate iterating the construction of $C^{*}$, the L-like inner model constructed using first order logic augmented with the “cofinality $\omega $ ” quantifier. We first show that $\left (C^{*}\right )^{C^{*}}=C^{*}\ne L$ is equiconsistent with $\mathrm {ZFC}$, as well as having finite strictly decreasing sequences of iterated $C^{*}$ s. We then show that in models of the form $L[U]$ we get infinite decreasing sequences of length $\omega $, and that an inner model with a measurable cardinal is required for that.
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  • 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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  • Generalizations of the Kunen inconsistency.Joel David Hamkins, Greg Kirmayer & Norman Lewis Perlmutter - 2012 - Annals of Pure and Applied Logic 163 (12):1872-1890.
    We present several generalizations of the well-known Kunen inconsistency that there is no nontrivial elementary embedding from the set-theoretic universe V to itself. For example, there is no elementary embedding from the universe V to a set-forcing extension V[G], or conversely from V[G] to V, or more generally from one set-forcing ground model of the universe to another, or between any two models that are eventually stationary correct, or from V to HOD, or conversely from HOD to V, or indeed (...)
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  • 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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  • Lifting elementary embeddings j: V λ → V λ. [REVIEW]Paul Corazza - 2007 - Archive for Mathematical Logic 46 (2):61-72.
    We describe a fairly general procedure for preserving I3 embeddings j: V λ → V λ via λ-stage reverse Easton iterated forcings. We use this method to prove that, assuming the consistency of an I3 embedding, V = HOD is consistent with the theory ZFC + WA where WA is an axiom schema in the language {∈, j} asserting a strong but not inconsistent form of “there is an elementary embedding V → V”. This improves upon an earlier result in (...)
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  • Lifting elementary embeddings j: Vλ → Vλ.Paul Corazza - 2007 - Archive for Mathematical Logic 46 (2):61-72.
    We describe a fairly general procedure for preserving I3 embeddings j: Vλ → Vλ via λ-stage reverse Easton iterated forcings. We use this method to prove that, assuming the consistency of an I3 embedding, V = HOD is consistent with the theory ZFC + WA where WA is an axiom schema in the language {∈, j} asserting a strong but not inconsistent form of “there is an elementary embedding V → V”. This improves upon an earlier result in which consistency (...)
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