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  1. Changing cardinal invariants of the reals without changing cardinals or the reals.Heike Mildenberger - 1998 - Journal of Symbolic Logic 63 (2):593-599.
    We show: The procedure mentioned in the title is often impossible. It requires at least an inner model with a measurable cardinal. The consistency strength of changing b and d from a regular κ to some regular δ < κ is a measurable of Mitchell order δ. There is an application to Cichon's diagram.
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  • Changing cardinal invariants of the reals without changing cardinals or the reals.Heike Mildenberger - 1998 - Journal of Symbolic Logic 63 (2):593-599.
    We show: The procedure mentioned in the title is often impossible. It requires at least an inner model with a measurable cardinal. The consistency strength of changingandfrom a regularκto some regularδ<κis a measurable of Mitchell orderδ. There is an application to Cichoń's diagram.
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  • Supplements of bounded permutation groups.Stephen Bigelow - 1998 - Journal of Symbolic Logic 63 (1):89-102.
    Let λ ≤ κ be infinite cardinals and let Ω be a set of cardinality κ. The bounded permutation group B λ (Ω), or simply B λ , is the group consisting of all permutations of Ω which move fewer than λ points in Ω. We say that a permutation group G acting on Ω is a supplement of B λ if B λ G is the full symmetric group on Ω. In [7], Macpherson and Neumann claimed to have classified (...)
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  • Supplements of bounded permutation groups.Stephen Bigelow - 1998 - Journal of Symbolic Logic 63 (1):89-102.
    Let λ ≤ κ be infinite cardinals and let Ω be a set of cardinality κ. The bounded permutation groupBλ(Ω), or simplyBλ, is the group consisting of all permutations of Ω which move fewer than λ points in Ω. We say that a permutation groupGacting on Ω is asupplement of BλifBλGis the full symmetric group on Ω.In [7], Macpherson and Neumann claimed to have classified all supplements of bounded permutation groups. Specifically, they claimed to have proved that a groupGacting on (...)
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  • More on the cut and choose game.Jindřich Zapletal - 1995 - Annals of Pure and Applied Logic 76 (3):291-301.
    The cut and choose game is one of the infinitary games on a complete Boolean algebra B introduced by Jech. We prove that existence of a winning strategy for II in implies semiproperness of B. If the existence of a supercompact cardinal is consistent then so is “for every 1-distributive algebra B II has a winning strategy in ”.
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  • On the transversal hypothesis and the weak Kurepa hypothesis.D. J. Walker - 1988 - Journal of Symbolic Logic 53 (3):854-877.
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  • Chang's model and covering properties.Claude Sureson - 1989 - Annals of Pure and Applied Logic 42 (1):45-79.
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  • About Prikry generic extensions.Claude Sureson - 1991 - Annals of Pure and Applied Logic 51 (3):247-278.
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  • The Jensen covering property.E. Schimmerling & W. H. Woodin - 2001 - Journal of Symbolic Logic 66 (4):1505-1523.
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  • On the consistency strength of the Milner–Sauer conjecture.Assaf Rinot - 2006 - Annals of Pure and Applied Logic 140 (1):110-119.
    In their paper from 1981, Milner and Sauer conjectured that for any poset P,≤, if , then P must contain an antichain of cardinality κ. The conjecture is consistent and known to follow from GCH-type assumptions. We prove that the conjecture has large cardinals consistency strength in the sense that its negation implies, for example, the existence of a measurable cardinal in an inner model. We also prove that the conjecture follows from Martin’s Maximum and holds for all singular λ (...)
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  • The covering lemma up to a Woodin cardinal.W. J. Mitchell, E. Schimmerling & J. R. Steel - 1997 - Annals of Pure and Applied Logic 84 (2):219-255.
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  • Inner models from extended logics: Part 1.Juliette Kennedy, Menachem Magidor & Jouko Väänänen - 2020 - Journal of Mathematical Logic 21 (2):2150012.
    If we replace first-order logic by second-order logic in the original definition of Gödel’s inner model L, we obtain the inner model of hereditarily ordinal definable sets [33]. In this paper...
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  • Smooth categories and global □.Ronald B. Jensen & Martin Zeman - 2000 - Annals of Pure and Applied Logic 102 (1-2):101-138.
    We shall construct a smooth category of mice and embeddings in the core model for measures of order 0. The existence of such a category implies that the global principle □ holds in K. We then prove a much stronger, the so-called condensation-coherent version of global □. The key tool of the whole construction is a new criterion on preserving soundness under condensation.
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  • $K$ without the measurable.Ronald Jensen & John Steel - 2013 - Journal of Symbolic Logic 78 (3):708-734.
    We show in ZFC that if there is no proper class inner model with a Woodin cardinal, then there is an absolutely definablecore modelthat is close toVin various ways.
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  • Singular cardinals and the pcf theory.Thomas Jech - 1995 - Bulletin of Symbolic Logic 1 (4):408-424.
    §1. Introduction. Among the most remarkable discoveries in set theory in the last quarter century is the rich structure of the arithmetic of singular cardinals, and its deep relationship to large cardinals. The problem of finding a complete set of rules describing the behavior of the continuum function 2ℵα for singular ℵα's, known as the Singular Cardinals Problem, has been attacked by many different techniques, involving forcing, large cardinals, inner models, and various combinatorial methods. The work on the singular cardinals (...)
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  • Hierarchies of Forcing Axioms II.Itay Neeman - 2008 - Journal of Symbolic Logic 73 (2):522 - 542.
    A $\Sigma _{1}^{2}$ truth for λ is a pair 〈Q, ψ〉 so that Q ⊆ Hλ, ψ is a first order formula with one free variable, and there exists B ⊆ Hλ+ such that (Hλ+; ε, B) $(H_{\lambda +};\in ,B)\vDash \psi [Q]$ . A cardinal λ is $\Sigma _{1}^{2}$ indescribable just in case that for every $\Sigma _{1}^{2}$ truth 〈Q, ψ〉 for λ, there exists $\overline{\lambda}<\lambda $ so that $\overline{\lambda}$ is a cardinal and $\langle Q\cap H_{\overline{\lambda}},\psi \rangle $ is a (...)
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  • The consistency strength of projective absoluteness.Kai Hauser - 1995 - Annals of Pure and Applied Logic 74 (3):245-295.
    It is proved that in the absence of proper class inner models with Woodin cardinals, for each n ε {1,…,ω}, ∑3 + n1 absoluteness implies there are n strong cardinals in K (where this denotes a suitably defined global version of the core model for one Woodin cardinal as exposed by Steel. Combined with a forcing argument of Woodin, this establishes that the consistency strength of ∑3 + n1 absoluteness is exactly that of n strong cardinals so that in particular (...)
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  • Strong cardinals in the core model.Kai Hauser & Greg Hjorth - 1997 - Annals of Pure and Applied Logic 83 (2):165-198.
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  • Indiscernible sequences for extenders, and the singular cardinal hypothesis.Moti Gitik & William J. Mitchell - 1996 - Annals of Pure and Applied Logic 82 (3):273-316.
    We prove several results giving lower bounds for the large cardinal strength of a failure of the singular cardinal hypothesis. The main result is the following theorem: Theorem. Suppose κ is a singular strong limit cardinal and 2κ λ where λ is not the successor of a cardinal of cofinality at most κ. If cf > ω then it follows that o λ, and if cf = ωthen either o λ or {α: K o α+n} is confinal in κ for (...)
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  • On the consistency strength of ‘Accessible’ Jonsson Cardinals and of the Weak Chang Conjecture.Hans-Dieter Donder & Peter Koepke - 1983 - Annals of Pure and Applied Logic 25 (3):233-261.
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  • The covering lemma for L[U].A. J. Dodd & R. B. Jensen - 1982 - Annals of Mathematical Logic 22 (2):127-135.
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