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  1.  15
    Compactness versus hugeness at successor cardinals.Sean Cox & Monroe Eskew - 2022 - Journal of Mathematical Logic 23 (1).
    If [Formula: see text] is regular and [Formula: see text], then the existence of a weakly presaturated ideal on [Formula: see text] implies [Formula: see text]. This partially answers a question of Foreman and Magidor about the approachability ideal on [Formula: see text]. As a corollary, we show that if there is a presaturated ideal [Formula: see text] on [Formula: see text] such that [Formula: see text] is semiproper, then CH holds. We also show some barriers to getting the tree (...)
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  2.  16
    Embeddings Into Outer Models.Monroe Eskew & Sy-David Friedman - 2022 - Journal of Symbolic Logic 87 (4):1301-1321.
    We explore the possibilities for elementary embeddings $j : M \to N$, where M and N are models of ZFC with the same ordinals, $M \subseteq N$, and N has access to large pieces of j. We construct commuting systems of such maps between countable transitive models that are isomorphic to various canonical linear and partial orders, including the real line ${\mathbb R}$.
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  3.  17
    Local saturation and square everywhere.Monroe Eskew - 2020 - Journal of Mathematical Logic 20 (3):2050019.
    We show that it is consistent relative to a huge cardinal that for all infinite cardinals [Formula: see text], [Formula: see text] holds and there is a stationary [Formula: see text] such that [Formula: see text] is [Formula: see text]-saturated.
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  4.  21
    Weak saturation properties and side conditions.Monroe Eskew - 2024 - Annals of Pure and Applied Logic 175 (1):103356.
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  5.  21
    Mutually embeddable models of ZFC.Monroe Eskew, Sy-David Friedman, Yair Hayut & Farmer Schlutzenberg - 2024 - Annals of Pure and Applied Logic 175 (1):103325.
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  6.  30
    Generic large cardinals as axioms.Monroe Eskew - 2020 - Review of Symbolic Logic 13 (2):375-387.
    We argue against Foreman’s proposal to settle the continuum hypothesis and other classical independent questions via the adoption of generic large cardinal axioms.
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  7.  11
    Incompatibility of Generic Hugeness Principles.Monroe Eskew - 2023 - Bulletin of Symbolic Logic 29 (2):157-162.
    We show that the weakest versions of Foreman’s minimal generic hugeness axioms cannot hold simultaneously on adjacent cardinals. Moreover, conventional forcing techniques cannot produce a model of one of these axioms.
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  8.  8
    On a strengthening of Jónssonness for ℵω.Monroe Eskew - 2020 - Mathematical Logic Quarterly 66 (2):235-238.
    We discuss a system of strengthenings of “ is Jónsson” indexed by real numbers, and identify a strongest one. We give a proof of a theorem of Silver and show that there is a barrier to weakening its hypothesis.
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