10 found
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  1.  31
    Iterability for (transfinite) stacks.Farmer Schlutzenberg - 2021 - Journal of Mathematical Logic 21 (2):2150008.
    We establish natural criteria under which normally iterable premice are iterable for stacks of normal trees. Let Ω be a regular uncountable cardinal. Let m < ω and M be an m-sound premouse and Σ be...
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  2.  18
    Reinhardt cardinals and iterates of V.Farmer Schlutzenberg - 2022 - Annals of Pure and Applied Logic 173 (2):103056.
  3.  14
    The definability of E in self-iterable mice.Farmer Schlutzenberg - 2023 - Annals of Pure and Applied Logic 174 (2):103208.
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  4.  12
    A premouse inheriting strong cardinals from V.Farmer Schlutzenberg - 2020 - Annals of Pure and Applied Logic 171 (9):102826.
  5.  9
    The Definability of the Extender Sequence From In.Farmer Schlutzenberg - 2024 - Journal of Symbolic Logic 89 (2):427-459.
    Let M be a short extender mouse. We prove that if $E\in M$ and $M\models $ “E is a countably complete short extender whose support is a cardinal $\theta $ and $\mathcal {H}_\theta \subseteq \mathrm {Ult}(V,E)$ ”, then E is in the extender sequence $\mathbb {E}^M$ of M. We also prove other related facts, and use them to establish that if $\kappa $ is an uncountable cardinal of M and $\kappa ^{+M}$ exists in M then $(\mathcal {H}_{\kappa ^+})^M$ satisfies the (...)
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  6.  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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  7.  9
    On the consistency of ZF with an elementary embedding from Vλ+2 into Vλ+2.Farmer Schlutzenberg - forthcoming - Journal of Mathematical Logic.
    According to a theorem due to Kenneth Kunen, under ZFC, there is no ordinal [Formula: see text] and nontrivial elementary embedding [Formula: see text]. His proof relied on the Axiom of Choice (AC), and no proof from ZF alone is has been discovered. [Formula: see text] is the assertion, introduced by Hugh Woodin, that [Formula: see text] is an ordinal and there is an elementary embedding [Formula: see text] with critical point [Formula: see text]. And [Formula: see text] asserts that (...)
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  8.  33
    Homogeneously Suslin sets in tame mice.Farmer Schlutzenberg - 2012 - Journal of Symbolic Logic 77 (4):1122-1146.
    This paper studies homogeneously Suslin (hom) sets of reals in tame mice. The following results are established: In 0 ¶ the hom sets are precisely the [Symbol] sets. In M n every hom set is correctly [Symbol] and (δ + 1)-universally Baire where ä is the least Woodin. In M u every hom set is <λ-hom, where λ is the supremum of the Woodins.
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  9.  13
    A Long Pseudo-Comparison of Premice in L[x].Farmer Schlutzenberg - 2018 - Notre Dame Journal of Formal Logic 59 (4):599-604.
    A significant open problem in inner model theory is the analysis of HODL[x] as a strategy premouse, for a Turing cone of reals x. We describe here an obstacle to such an analysis. Assuming sufficient large cardinals, for a Turing cone of reals x there are proper class 1-small premice M,N, with Woodin cardinals δ,ε, respectively, such that M|δ and N|ε are in L[x], M and N are countable in L[x], and the pseudo-comparison of M with N succeeds, is in (...)
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  10.  17
    Choice principles in local mantles.Farmer Schlutzenberg - 2022 - Mathematical Logic Quarterly 68 (3):264-278.
    Assume. Let κ be a cardinal. A ‐ground is a transitive proper class W modelling such that V is a generic extension of W via a forcing of cardinality. The κ‐mantle is the intersection of all ‐grounds. We prove that certain partial choice principles in are the consequence of κ being inaccessible/weakly compact, and some other related facts.
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