26 found
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John Steel [17]John R. Steel [14]
  1. Does Mathematics Need New Axioms.Solomon Feferman, Harvey M. Friedman, Penelope Maddy & John R. Steel - 1999 - Bulletin of Symbolic Logic 6 (4):401-446.
    Part of the ambiguity lies in the various points of view from which this question might be considered. The crudest di erence lies between the point of view of the working mathematician and that of the logician concerned with the foundations of mathematics. Now some of my fellow mathematical logicians might protest this distinction, since they consider themselves to be just more of those \working mathematicians". Certainly, modern logic has established itself as a very respectable branch of mathematics, and there (...)
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  2.  42
    PFA Implies ADL(R).John R. Steel - 2005 - Journal of Symbolic Logic 70 (4):1255 - 1296.
  3.  49
    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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  4. Mathematics Needs New Axioms.John Steel - 2000 - Bulletin of Symbolic Logic 6 (4):422-433.
  5.  5
    $K$ 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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  6.  44
    HOD L(ℝ) is a Core Model Below Θ.John R. Steel - 1995 - Bulletin of Symbolic Logic 1 (1):75-84.
    In this paper we shall answer some questions in the set theory of L, the universe of all sets constructible from the reals. In order to do so, we shall assume ADL, the hypothesis that all 2-person games of perfect information on ω whose payoff set is in L are determined. This is by now standard practice. ZFC itself decides few questions in the set theory of L, and for reasons we cannot discuss here, ZFC + ADL yields the most (...)
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  7.  27
    The Self-Iterability of L[E].Ralf Schindler & John Steel - 2009 - Journal of Symbolic Logic 74 (3):751-779.
    Let L[E] be an iterable tame extender model. We analyze to which extent L[E] knows fragments of its own iteration strategy. Specifically, we prove that inside L[E], for every cardinal K which is not a limit of Woodin cardinals there is some cutpoint t K > a>ω1 are cardinals, then ◊$_{K.\lambda }^* $ holds true, and if in addition λ is regular, then ◊$_{K.\lambda }^* $ holds true.
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  8.  19
    Deconstructing Inner Model Theory.Ralf-Dieter Schindler, John Steel & Martin Zeman - 2002 - Journal of Symbolic Logic 67 (2):721-736.
  9.  55
    A Weak Dodd-Jensen Lemma.Itay Neeman & John Steel - 1999 - Journal of Symbolic Logic 64 (3):1285-1294.
    We show that every sufficiently iterable countable mouse has a unique iteration strategy whose associated iteration maps are lexicographically minimal. This enables us to extend the results of [3] on the good behavior of the standard parameter from tame mice to arbitrary mice.
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  10.  7
    Equiconsistencies at Subcompact Cardinals.Itay Neeman & John Steel - 2016 - Archive for Mathematical Logic 55 (1-2):207-238.
    We present equiconsistency results at the level of subcompact cardinals. Assuming SBHδ, a special case of the Strategic Branches Hypothesis, we prove that if δ is a Woodin cardinal and both □ and □δ fail, then δ is subcompact in a class inner model. If in addition □ fails, we prove that δ is Π12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi_1^2}$$\end{document} subcompact in a class inner model. These results are optimal, and lead to equiconsistencies. As a corollary (...)
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  11.  33
    Complementation in the Turing Degrees.Theodore A. Slaman & John R. Steel - 1989 - Journal of Symbolic Logic 54 (1):160-176.
    Posner [6] has shown, by a nonuniform proof, that every ▵ 0 2 degree has a complement below 0'. We show that a 1-generic complement for each ▵ 0 2 set of degree between 0 and 0' can be found uniformly. Moreover, the methods just as easily can be used to produce a complement whose jump has the degree of any real recursively enumerable in and above $\varnothing'$ . In the second half of the paper, we show that the complementation (...)
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  12.  8
    The Mouse Set Conjecture for Sets of Reals.Grigor Sargsyan & John Steel - 2015 - Journal of Symbolic Logic 80 (2):671-683.
  13.  15
    A Classification of Jump Operator.John R. Steel - 1982 - Journal of Symbolic Logic 47 (2):347-358.
  14.  14
    Descending Sequences of Degrees.John Steel - 1975 - Journal of Symbolic Logic 40 (1):59-61.
  15.  64
    Counterexamples to the Unique and Cofinal Branches Hypotheses.Itay Neeman & John Steel - 2006 - Journal of Symbolic Logic 71 (3):977 - 988.
    We produce counterexamples to the unique and cofinal branches hypotheses, assuming (slightly less than) the existence of a cardinal which is strong past a Woodin cardinal.
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  16. Covering Properties of Core Models.Ernest Schimmerling, Peter Koepke, William J. Mitchell & John R. Steel - 2004 - Bulletin of Symbolic Logic 10 (4):583-588.
  17.  25
    Moscone Center West, San Francisco, CA January 15–16, 2010.Fernando J. Ferreira, John Harrison, François Loeser, Chris Miller, Joseph S. Miller, Slawomir J. Solecki, Stevo Todorcevic & John Steel - 2010 - Bulletin of Symbolic Logic 16 (3).
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  18.  20
    Distinct Iterable Branches.John R. Steel - 2005 - Journal of Symbolic Logic 70 (4):1127 - 1136.
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  19. Notre Dame, Indiana May 20–May 23, 2009.Patricia Blanchette, Heike Mildenberger, André Nies, Anand Pillay, Alexander Razborov, Alexandra Shlapentokh, John R. Steel & Boris Zilber - 2009 - Bulletin of Symbolic Logic 15 (4).
     
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  20.  12
    Scales on Σ 1 1 Sets.John R. Steel, A. S. Kechris, D. A. Martin, Y. N. Moschovakis, Yiannis N. Moschovakis & Donald A. Martin - 1992 - Journal of Symbolic Logic 57 (1):261-262.
  21. 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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  22.  3
    2009–2010 Winter Meeting of the Association for Symbolic Logic.John Steel - 2010 - Bulletin of Symbolic Logic 16 (3):430-437.
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  23.  4
    2009-2010 Winter Meeting of the Association for Symbolic Logic.John Steel - 2010 - Bulletin of Symbolic Logic 16 (3):430-437.
  24.  12
    HOD L(ℝ) is a Core Model Below Θ.John R. Steel - 1995 - Bulletin of Symbolic Logic 1 (1):75-84.
    In this paper we shall answer some questions in the set theory of L, the universe of all sets constructible from the reals. In order to do so, we shall assume ADL, the hypothesis that all 2-person games of perfect information on ω whose payoff set is in L are determined. This is by now standard practice. ZFC itself decides few questions in the set theory of L, and for reasons we cannot discuss here, ZFC + ADL yields the most (...)
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  25.  18
    Determinateness and the Separation Property.John R. Steel - 1981 - Journal of Symbolic Logic 46 (1):41-44.
  26.  6
    How to Win Some Simple Iteration Games.Alessandro Andretta & John Steel - 1997 - Annals of Pure and Applied Logic 83 (2):103-164.
    We introduce two new iteration games: the game , which is a strengthening of the weak iteration game, and the game , which is somewhat stronger than but weaker than the full iteration game of length ω1. For a countable M elementarily embeddable in some Vη, with two players I and II, we can show that II wins and that I does not win.
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