11 found
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  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.  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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  4.  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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  5.  15
    A Classification of Jump Operator.John R. Steel - 1982 - Journal of Symbolic Logic 47 (2):347-358.
  6. Covering Properties of Core Models.Ernest Schimmerling, Peter Koepke, William J. Mitchell & John R. Steel - 2004 - Bulletin of Symbolic Logic 10 (4):583-588.
  7.  20
    Distinct Iterable Branches.John R. Steel - 2005 - Journal of Symbolic Logic 70 (4):1127 - 1136.
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  8. 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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  9.  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.
  10.  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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  11.  18
    Determinateness and the Separation Property.John R. Steel - 1981 - Journal of Symbolic Logic 46 (1):41-44.