21 found
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  1.  30
    Square in core models.Ernest Schimmerling & Martin Zeman - 2001 - Bulletin of Symbolic Logic 7 (3):305-314.
    We prove that in all Mitchell-Steel core models, □ κ holds for all κ. (See Theorem 2.). From this we obtain new consistency strength lower bounds for the failure of □ κ if κ is either singular and countably closed, weakly compact, or measurable. (Corallaries 5, 8, and 9.) Jensen introduced a large cardinal property that we call subcompactness; it lies between superstrength and supercompactness in the large cardinal hierarchy. We prove that in all Jensen core models, □ κ holds (...)
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  2.  23
    Characterization of □κin core models.Ernest Schimmerling & Martin Zeman - 2004 - Journal of Mathematical Logic 4 (01):1-72.
    We present a general construction of a □κ-sequence in Jensen's fine structural extender models. This construction yields a local definition of a canonical □κ-sequence as well as a characterization of those cardinals κ, for which the principle □κ fails. Such cardinals are called subcompact and can be described in terms of elementary embeddings. Our construction is carried out abstractly, making use only of a few fine structural properties of levels of the model, such as solidity and condensation.
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  3.  31
    Deconstructing inner model theory.Ralf-Dieter Schindler, John Steel & Martin Zeman - 2002 - Journal of Symbolic Logic 67 (2):721-736.
  4.  16
    Ideal projections and forcing projections.Sean Cox & Martin Zeman - 2014 - Journal of Symbolic Logic 79 (4):1247-1285.
    It is well known that saturation of ideals is closely related to the “antichain-catching” phenomenon from Foreman–Magidor–Shelah [10]. We consider several antichain-catching properties that are weaker than saturation, and prove:If${\cal I}$is a normal ideal on$\omega _2 $which satisfiesstationary antichain catching, then there is an inner model with a Woodin cardinal;For any$n \in \omega $, it is consistent relative to large cardinals that there is a normal ideal${\cal I}$on$\omega _n $which satisfiesprojective antichain catching, yet${\cal I}$is not saturated. This provides a negative (...)
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  5.  25
    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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  6.  16
    Two Upper Bounds on Consistency Strength of $negsquare{aleph_{omega}}$ and Stationary Set Reflection at Two Successive $aleph{n}$.Martin Zeman - 2017 - Notre Dame Journal of Formal Logic 58 (3):409-432.
    We give modest upper bounds for consistency strengths for two well-studied combinatorial principles. These bounds range at the level of subcompact cardinals, which is significantly below a κ+-supercompact cardinal. All previously known upper bounds on these principles ranged at the level of some degree of supercompactness. We show that by using any of the standard modified Prikry forcings it is possible to turn a measurable subcompact cardinal into ℵω and make the principle □ℵω,<ω fail in the generic extension. We also (...)
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  7.  34
    More fine structural global square sequences.Martin Zeman - 2009 - Archive for Mathematical Logic 48 (8):825-835.
    We extend the construction of a global square sequence in extender models from Zeman [8] to a construction of coherent non-threadable sequences and give a characterization of stationary reflection at inaccessibles similar to Jensen’s characterization in L.
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  8.  9
    Global square sequences in extender models.Martin Zeman - 2010 - Annals of Pure and Applied Logic 161 (7):956-985.
    We present a construction of a global square sequence in extender models with λ-indexing.
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  9.  10
    Dodd parameters and λ-indexing of extenders.Martin Zeman - 2004 - Journal of Mathematical Logic 4 (01):73-108.
    We study generalizations of Dodd parameters and establish their fine structural properties in Jensen extender models with λ-indexing. These properties are one of the key tools in various combinatorial constructions, such as constructions of square sequences and morasses.
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  10.  14
    ◇ at Mahlo cardinals.Martin Zeman - 2000 - Journal of Symbolic Logic 65 (4):1813-1822.
  11.  33
    $\Diamond$ at mahlo cardinals.Martin Zeman - 2000 - Journal of Symbolic Logic 65 (4):1813 - 1822.
    Given a Mahlo cardinal κ and a regular ε such that $\omega_1 we show that $\diamond_\kappa (cf = \epsilon)$ holds in V provided that there are only non-stationarily many $\beta , with o(β) ≥ ε in K.
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  12.  12
    Games with filters I.Matthew Foreman, Menachem Magidor & Martin Zeman - forthcoming - Journal of Mathematical Logic.
    This paper has two parts. The first is concerned with a variant of a family of games introduced by Holy and Schlicht, that we call Welch games. Player II having a winning strategy in the Welch game of length [Formula: see text] on [Formula: see text] is equivalent to weak compactness. Winning the game of length [Formula: see text] is equivalent to [Formula: see text] being measurable. We show that for games of intermediate length [Formula: see text], II winning implies (...)
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  13.  8
    Downward transference of mice and universality of local core models.Andrés Eduardo Caicedo & Martin Zeman - 2017 - Journal of Symbolic Logic 82 (2):385-419.
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  14.  21
    Cardinal transfer properties in extender models.Ernest Schimmerling & Martin Zeman - 2008 - Annals of Pure and Applied Logic 154 (3):163-190.
    We prove that if image is a Jensen extender model, then image satisfies the Gap-1 morass principle. As a corollary to this and a theorem of Jensen, the model image satisfies the Gap-2 Cardinal Transfer Property → for all infinite cardinals κ and λ.
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  15. REVIEWS-Various articles on models.Martin Zeman - 2004 - Bulletin of Symbolic Logic 10 (4):583-587.
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  16.  17
    Ernest Schimmerling. Covering properties of core models. Sets and proofs. (Leeds, 1997), London Mathematical Society Lecture Note Series 258. Cambridge University Press, Cambridge, 1999, pp. 281–299. - Peter Koepke. An introduction to extenders and core models for extender sequences. Logic Colloquium '87 (Granada, 1987), Studies in Logic and the Foundations of Mathematics 129. North-Holland, Amsterdam, 1989, pp. 137–182. - William J. Mitchell. The core model up to a Woodin cardinal. Logic, methodology and philosophy of science, IX (Uppsala, 1991), Studies in Logic and the Foundations of Mathematics 134, North-Holland, Amsterdam, 1994, pp. 157–175. - Benedikt Löwe and John R. Steel. An introduction to core model theory. Sets and proofs (Leeds, 1997), London Mathematical Society Lecture Note Series 258, Cambridge University Press, Cambridge, 1999, pp. 103–157. - John R. Steel. Inner models with many Woodin cardinals. Annals of Pure and Applied Logic, vol. 65 no. 2 (1993), pp. 185–209. -.Martin Zeman - 2004 - Bulletin of Symbolic Logic 10 (4):583-588.
  17. WJ Mitchell, I [ω2] can be the nonstationary ideal on Cof (ω1).Martin Zeman - 2011 - Bulletin of Symbolic Logic 17 (4):535.
  18.  28
    A characterization of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square(\kappa^{+})}$$\end{document} in extender models. [REVIEW]Kyriakos Kypriotakis & Martin Zeman - 2013 - Archive for Mathematical Logic 52 (1-2):67-90.
    We prove that, in any fine structural extender model with Jensen’s λ-indexing, there is a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square(\kappa^{+})}$$\end{document} -sequence if and only if there is a pair of stationary subsets of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa^{+} \cap {\rm {cof}}( < \kappa)}$$\end{document} without common reflection point of cofinality \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${ < \kappa}$$\end{document} which, in turn, is equivalent to the existence of a (...)
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  19.  12
    Ernest Schimmerling. Covering properties of core models. Sets and proofs. , London Mathematical Society Lecture Note Series 258. Cambridge University Press, Cambridge, 1999, pp. 281–299. - Peter Koepke. An introduction to extenders and core models for extender sequences. Logic Colloquium '87 , Studies in Logic and the Foundations of Mathematics 129. North-Holland, Amsterdam, 1989, pp. 137–182. - William J. Mitchell. The core model up to a Woodin cardinal. Logic, methodology and philosophy of science, IX , Studies in Logic and the Foundations of Mathematics 134, North-Holland, Amsterdam, 1994, pp. 157–175. - Benedikt Löwe and John R. Steel. An introduction to core model theory. Sets and proofs , London Mathematical Society Lecture Note Series 258, Cambridge University Press, Cambridge, 1999, pp. 103–157. - John R. Steel. Inner models with many Woodin cardinals. Annals of Pure and Applied Logic, vol. 65 no. 2 , pp. 185–209. - Ernest Schimmerling. Combinatorial principles in the core mode. [REVIEW]Martin Zeman - 2004 - Bulletin of Symbolic Logic 10 (4):583-588.
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  20.  10
    William J. Mitchell. I[ω2] can be the nonstationary ideal on Cof . Transactions of the American Mathematical Society, vol. 361 , no. 2, pp. 561–601. [REVIEW]Martin Zeman - 2011 - Bulletin of Symbolic Logic 17 (4):535-537.
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  21.  4
    William J. Mitchell. I_[ω 2 ] _can be the nonstationary ideal on Cof (ω 1 ). Transactions of the American Mathematical Society, vol. 361 (2009), no. 2, pp. 561–601. [REVIEW]Martin Zeman - 2011 - Bulletin of Symbolic Logic 17 (4):535-537.
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