27 found
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  1.  12
    Combinatorial Principles in the Core Model for One Woodin Cardinal.Ernest Schimmerling - 1995 - Annals of Pure and Applied Logic 74 (2):153-201.
    We study the fine structure of the core model for one Woodin cardinal, building of the work of Mitchell and Steel on inner models of the form . We generalize to some combinatorial principles that were shown by Jensen to hold in L. We show that satisfies the statement: “□κ holds whenever κ the least measurable cardinal λ of order λ++”. We introduce a hierarchy of combinatorial principles □κ, λ for 1 λ κ such that □κ□κ, 1 □κ, λ □κ, (...)
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  2.  7
    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.  15
    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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  4.  31
    Stacking Mice.Ronald Jensen, Ernest Schimmerling, Ralf Schindler & John Steel - 2009 - Journal of Symbolic Logic 74 (1):315-335.
    We show that either of the following hypotheses imply that there is an inner model with a proper class of strong cardinals and a proper class of Woodin cardinals. 1) There is a countably closed cardinal k ≥ N₃ such that □k and □(k) fail. 2) There is a cardinal k such that k is weakly compact in the generic extension by Col(k, k⁺). Of special interest is 1) with k = N₃ since it follows from PFA by theorems of (...)
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  5.  18
    An Equiconsistency Result on Partial Squares.John Krueger & Ernest Schimmerling - 2011 - Journal of Mathematical Logic 11 (1):29-59.
    We prove that the following two statements are equiconsistent: there exists a greatly Mahlo cardinal; there exists a regular uncountable cardinal κ such that no stationary subset of κ+ ∩ cof carries a partial square.
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  6.  7
    John R. Steel. The Core Model Iterability Problem. Lecture Notes in Logic, No. 8. Springer, Berlin, Heidelberg, New York, Etc., 1996, Iii + 112 Pp. [REVIEW]Ernest Schimmerling - 1998 - Journal of Symbolic Logic 63 (1):326-328.
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  7.  18
    Collapsing Functions.Ernest Schimmerling & Boban Velickovic - 2004 - Mathematical Logic Quarterly 50 (1):3-8.
    We define what it means for a function on ω1 to be a collapsing function for λ and show that if there exists a collapsing function for +, then there is no precipitous ideal on ω1. We show that a collapsing function for ω2 can be added by forcing. We define what it means to be a weakly ω1-Erdös cardinal and show that in L[E], there is a collapsing function for λ iff λ is less than the least weakly ω1-Erdös (...)
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  8.  28
    Hierarchies of Forcing Axioms I.Itay Neeman & Ernest Schimmerling - 2008 - Journal of Symbolic Logic 73 (1):343-362.
    We prove new upper bound theorems on the consistency strengths of SPFA (θ), SPFA(θ-linked) and SPFA(θ⁺-cc). Our results are in terms of (θ, Γ)-subcompactness, which is a new large cardinal notion that combines the ideas behind subcompactness and Γ-indescribability. Our upper bound for SPFA(c-linked) has a corresponding lower bound, which is due to Neeman and appears in his follow-up to this paper. As a corollary, SPFA(c-linked) and PFA(c-linked) are each equiconsistent with the existence of a $\Sigma _{1}^{2}$ -indescribable cardinal. Our (...)
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  9.  29
    The Abc's of Mice.Ernest Schimmerling - 2001 - Bulletin of Symbolic Logic 7 (4):485-503.
  10.  26
    Some Calkin Algebras Have Outer Automorphisms.Ilijas Farah, Paul McKenney & Ernest Schimmerling - 2013 - Archive for Mathematical Logic 52 (5-6):517-524.
    We consider various quotients of the C*-algebra of bounded operators on a nonseparable Hilbert space, and prove in some cases that, assuming some restriction of the Generalized Continuum Hypothesis, there are many outer automorphisms.
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  11.  7
    Separating Weak Partial Square Principles.John Krueger & Ernest Schimmerling - 2014 - Annals of Pure and Applied Logic 165 (2):609-619.
    We introduce the weak partial square principles View the MathML source and View the MathML source, which combine the ideas of a weak square sequence and a partial square sequence. We construct models in which weak partial square principles fail. The main result of the paper is that □λ,κ does not imply View the MathML source.
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  12.  8
    A Finite Family Weak Square Principle.Ernest Schimmerling - 1999 - Journal of Symbolic Logic 64 (3):1087-1110.
  13.  31
    2001 Annual Meeting of the Association for Symbolic Logic.Joan Feigenbaum, Haim Gaifman, Jean-Yves Girard, C. Ward Henson, Denis Hirschfeldt, Carl G. Jockusch Jr, Saul Kripke, Salma Kuhlmann, John C. Mitchell & Ernest Schimmerling - 2001 - Bulletin of Symbolic Logic 7 (3):420-435.
  14.  10
    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.  10
    A Question About Suslin Trees and the Weak Square Hierarchy.Ernest Schimmerling - 2005 - Notre Dame Journal of Formal Logic 46 (3):373-374.
    We present a question about Suslin trees and the weak square hierarchy which was contributed to the list of open problems of the BIRS workshop.
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  16. The Covering Lemma Up to a Woodin Cardinal.William Mitchell, Ernest Schimmerling & John Steel - 2003 - Bulletin of Symbolic Logic 9 (3):414-416.
     
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  17.  13
    Diamond and Antichains.James Cummings & Ernest Schimmerling - 2004 - Archive for Mathematical Logic 44 (1):71-76.
    It is obvious that ♦ implies the existence of an antichain of stationary sets of cardinality which is the largest possible cardinality. We show that the obvious antichain is not maximal and find a less obvious extension of it by ℵ2 more stationary sets.
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  18.  16
    Copies of Books to Asl, Box 742, Vassar College, 124 Raymond Avenue, Poughkeepsie, Ny 12604, Usa. In a Review, a Reference “Jsl Xliii 148,” for Example, Refers Either to the Publication Reviewed on Page 148 of Volume 43 of the Journal, or to the Review Itself (Which Contains Full Bibliographical Information for the Reviewed Publication). Analogously, a Reference. [REVIEW]Anuj Dawar Colyvan, Steffen Lempp, Rahim Moosa, Ernest Schimmerling & Alex Simpson - 2013 - Bulletin of Symbolic Logic 19 (2).
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  19.  13
    Review: John R. Steel, The Core Model Iterability Problem. [REVIEW]Ernest Schimmerling - 1998 - Journal of Symbolic Logic 63 (1):326-328.
  20.  9
    Zeman Martin. Inner Models and Large Cardinals. De Gruyter Series in Logic and its Applications, Vol. 5. Walter de Gruyter and Co., Berlin, 2002, Xii+ 369 Pp. [REVIEW]Ernest Schimmerling - 2003 - Bulletin of Symbolic Logic 9 (2):234-235.
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  21.  7
    College, 124 Raymond Avenue, Poughkeepsie, Ny 12604, Usa. In a Review, a Reference “Jsl Xliii 148,” for Example, Refers Either to the Publication Reviewed on Page 148 of Volume 43 of the Journal, or to the Review Itself (Which Contains Full Bibliographical Information for the Reviewed Publication). Analogously, a Reference “Bsl VII 376” Refers to the Review Beginning on Page 376 in Volume 7 of This Bulletin, Or. [REVIEW]Mark Colyvan Burgess, Anuj Dawar, Marcelo Fiore, Noam Greenberg, Hannes Leitgeb, Ernest Schimmerling, Carsten Schürmann & Kai Wehmeier - 2010 - Bulletin of Symbolic Logic 16 (3).
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  22.  6
    Ny 12604, Usa.Anuj Dawar Colyvan, Noam Greenberg, Rahim Moosa, Ernest Schimmerling & Alex Simp - 2012 - Bulletin of Symbolic Logic 18 (4).
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  23.  6
    2010 North American Annual Meeting of the Association for Symbolic Logic.Alexander Razborov, Bob Coecke, Zoé Chatzidakis, Bjørn Kjos, Nicolaas P. Landsman, Lawrence S. Moss, Dilip Raghavan, Tom Scanlon, Ernest Schimmerling & Henry Towsner - 2011 - Bulletin of Symbolic Logic 17 (1):127-154.
  24.  6
    College, 124 Raymond Avenue, Poughkeepsie, Ny 12604, Usa. In a Review, a Reference “Jsl Xliii 148,” for Example, Refers Either to the Publication Reviewed on Page 148 of Volume 43 of the Journal, or to the Review Itself (Which Contains Full Bibliographical Information for the Reviewed Publication). Analogously, a Reference “Bsl VII 376” Refers to the Review Beginning on Page 376 in Volume 7 of This Bulletin, Or. [REVIEW]Anuj Dawar Colyvan, Marcelo Fiore, Noam Greenberg, Hannes Leitgeb, Rahim Moosa, Ernest Schimmerling, Carsten Schürmann & Kai Wehmeier - 2011 - Bulletin of Symbolic Logic 17 (1).
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  25.  3
    Inner Models and Large Cardinals.Ernest Schimmerling - 2003 - Bulletin of Symbolic Logic 9 (2):234-235.
  26. Covering Properties of Core Models.Ernest Schimmerling, Peter Koepke, William J. Mitchell & John R. Steel - 2004 - Bulletin of Symbolic Logic 10 (4):583-588.
  27. Ilijas Farah. All Automorphisms of the Calkin Algebra Are Inner. Annals of Mathematics, Vol. 173 , No. 2, Pp. 619–661.Ernest Schimmerling - 2011 - Bulletin of Symbolic Logic 17 (3):467-470.