34 found
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  1.  3
    Forcing with Sequences of Models of Two Types.Itay Neeman - 2014 - Notre Dame Journal of Formal Logic 55 (2):265-298.
    We present an approach to forcing with finite sequences of models that uses models of two types. This approach builds on earlier work of Friedman and Mitchell on forcing to add clubs in cardinals larger than $\aleph_{1}$, with finite conditions. We use the two-type approach to give a new proof of the consistency of the proper forcing axiom. The new proof uses a finite support forcing, as opposed to the countable support iteration in the standard proof. The distinction is important (...)
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  2.  1
    The Tree Property Up to אω+1.Itay Neeman - 2014 - Journal of Symbolic Logic 79 (2):429-459.
  3. Inner Models and Ultrafilters in L(R).Itay Neeman - 2007 - Bulletin of Symbolic Logic 13 (1):31-53.
    We present a characterization of supercompactness measures for ω1 in L(R), and of countable products of such measures, using inner models. We give two applications of this characterization, the first obtaining the consistency of $\delta_3^1 = \omega_2$ with $ZFC+AD^{L(R)}$ , and the second proving the uniqueness of the supercompactness measure over ${\cal P}_{\omega_1} (\lambda)$ in L(R) for $\lambda > \delta_1^2$.
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  4.  5
    Aronszajn Trees and Failure of the Singular Cardinal Hypothesis.Itay Neeman - 2009 - Journal of Mathematical Logic 9 (1):139-157.
  5.  20
    Optimal Proofs of Determinacy.Itay Neeman - 1995 - Bulletin of Symbolic Logic 1 (3):327-339.
  6.  3
    Inner Models in the Region of a Woodin Limit of Woodin Cardinals.Itay Neeman - 2002 - Annals of Pure and Applied Logic 116 (1-3):67-155.
    We extend the construction of Mitchell and Steel to produce iterable fine structure models which may contain Woodin limits of Woodin cardinals, and more. The precise level reached is that of a cardinal which is both a Woodin cardinal and a limit of cardinals strong past it.
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  7.  8
    A Criterion for Coarse Iterability.Gunter Fuchs, Itay Neeman & Ralf Schindler - 2010 - Archive for Mathematical Logic 49 (4):447-467.
    The main result of this paper is the following theorem: Let M be a premouse with a top extender, F. Suppose that (a) M is linearly coarsely iterable via hitting F and its images, and (b) if M * is a linear iterate of M as in (a), then M * is coarsely iterable with respect to iteration trees which do not use the top extender of M * and its images. Then M is coarsely iterable.
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  8.  43
    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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  9.  8
    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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  10.  8
    Proper Forcing and L(ℝ).Itay Neeman & Jindřich Zapletal - 2001 - Journal of Symbolic Logic 66 (2):801-810.
    We present two ways in which the model L(R) is canonical assuming the existence of large cardinals. We show that the theory of this model, with ordinal parameters, cannot be changed by small forcing; we show further that a set of ordinals in V cannot be added to L(R) by small forcing. The large cardinal needed corresponds to the consistency strength of AD L (R); roughly ω Woodin cardinals.
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  11.  5
    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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  12.  2
    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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  13.  1
    The Mitchell Order Below Rank-To-Rank.Itay Neeman - 2004 - Journal of Symbolic Logic 69 (4):1143 - 1162.
    We show that Mitchell order on downward closed extenders below rank-to-rank type is wellfounded.
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  14.  3
    Optimal Proofs of Determinacy II.Itay Neeman - 2002 - Journal of Mathematical Logic 2 (02):227-258.
  15.  14
    A Cardinal Preserving Extension Making the Set of Points of Countable V Cofinality Nonstationary.Moti Gitik, Itay Neeman & Dima Sinapova - 2007 - Archive for Mathematical Logic 46 (5-6):451-456.
    Assuming large cardinals we produce a forcing extension of V which preserves cardinals, does not add reals, and makes the set of points of countable V cofinality in κ+ nonstationary. Continuing to force further, we obtain an extension in which the set of points of countable V cofinality in ν is nonstationary for every regular ν ≥ κ+. Finally we show that our large cardinal assumption is optimal.
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  16.  2
    Unraveling Π11 Sets.Itay Neeman - 2000 - Annals of Pure and Applied Logic 106 (1-3):151-205.
    We construct coverings which unravel given Π11 sets. This in turn is used to prove, from optimal large cardinal assumptions, the determinacy of games with payoff and the determinacy of games with payoff in the σ algebra generated by Π11 sets.
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  17.  25
    The Strength of Blackwell Determinacy.Donald A. Martin, Itay Neeman & Marco Vervoort - 2003 - Journal of Symbolic Logic 68 (2):615-636.
    We show that Blackwell determinacy in L(R) implies determinacy in L(R).
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  18.  6
    Square Principles with Tail-End Agreement.William Chen & Itay Neeman - 2015 - Archive for Mathematical Logic 54 (3-4):439-452.
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  19.  2
    Equiconsistencies at Subcompact Cardinals.Itay Neeman & John Steel - 2016 - Archive for Mathematical Logic 55 (1-2):207-238.
  20.  8
    Effective Cardinals of Boldface Pointclasses.Alessandro Andretta, Greg Hjorth & Itay Neeman - 2007 - Journal of Mathematical Logic 7 (1):35-82.
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  21.  4
    1995–1996 Annual Meeting of the Association for Symbolic Logic.Tomek Bartoszynski, Harvey Friedman, Geoffrey Hellman, Bakhadyr Khoussainov, Phokion G. Kolaitis, Richard Shore, Charles Steinhorn, Mirna Dzamonja, Itay Neeman & Slawomir Solecki - 1996 - Bulletin of Symbolic Logic 2 (4):448-472.
  22.  3
    San Antonio Convention Center San Antonio, Texas January 14–15, 2006.Douglas Cenzer, C. Ward Henson, Michael C. Laskowski, Alain Louveau, Russell Miller, Itay Neeman, Sergei Starchenko & Valentina Harizanov - 2006 - Bulletin of Symbolic Logic 12 (4).
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  23.  2
    2001 European Summer Meeting of the Association for Symbolic Logic Logic Colloquium'01.Itay Neeman, Alexander Leitsch, Toshiyasu Arai, Steve Awodey, James Cummings, Rod Downey & Harvey Friedman - 2002 - Bulletin of Symbolic Logic 8 (1):111-180.
  24.  2
    Determinacy for Games Ending at the First Admissible Relative to the Play.Itay Neeman - 2006 - Journal of Symbolic Logic 71 (2):425 - 459.
    Let o(κ) denote the Mitchell order of κ. We show how to reduce long games which run to the first ordinal admissible in the play, to iteration games on models with a cardinal κ so that (1) κ is a limit of Woodin cardinals: and (2) o(κ) = κ⁺⁺. We use the reduction to derive several optimal determinacy results on games which run to the first admissible in the play.
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  25.  1
    2011 North American Annual Meeting of the Association for Symbolic Logic.Itay Neeman - 2012 - Bulletin of Symbolic Logic 18 (2):275-305.
  26.  3
    The Strength of Jullien's Indecomposability Theorem.Itay Neeman - 2008 - Journal of Mathematical Logic 8 (1):93-119.
  27.  1
    Mitchell William, Schimmerling Ernest, and Steel John. The Covering Lemma Up to a Woodin Cardinal. Annals of Pure and Applied Logic, Vol. 84 (1997), Pp. 219–255. [REVIEW]Itay Neeman - 2003 - Bulletin of Symbolic Logic 9 (3):414-416.
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  28.  2
    Finite State Automata and Monadic Definability of Singular Cardinals.Itay Neeman - 2008 - Journal of Symbolic Logic 73 (2):412 - 438.
    We define a class of finite state automata acting on transfinite sequences, and use these automata to prove that no singular cardinal can be defined by a monadic second order formula over the ordinals.
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  29.  1
    Games of Length Ω1.Itay Neeman - 2007 - Journal of Mathematical Logic 7 (1):83-124.
  30. Proper Forcings and Absoluteness in LProper Forcing and L.Paul B. Larson, Itay Neeman & Jindrich Zapletal - 2002 - Bulletin of Symbolic Logic 8 (4):548.
  31. REVIEWS-The Covering Lemma Up to a Woodin Cardinal.W. Mitchell, E. Schimmerling, J. Steel & Itay Neeman - 2003 - Bulletin of Symbolic Logic 9 (3):414-416.
  32. Annals of Pure and Applied Logic.Itay Neeman - 2003 - Bulletin of Symbolic Logic 9 (3):414-416.
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  33. Necessary Use of [Image] Induction in a Reversal.Itay Neeman - 2011 - Journal of Symbolic Logic 76 (2):561 - 574.
    Jullien's indecomposability theorem (INDEC) states that if a scattered countable linear order is indecomposable, then it is either indecomposable to the left, or indecomposable to the right. The theorem was shown by Montalbán to be a theorem of hyperarithmetic analysis, and then, in the base system RCA₀ plus ${\mathrm{\Sigma }}_{1}^{1}\text{\hspace{0.17em}}$ induction, it was shown by Neeman to have strength strictly between weak ${\mathrm{\Sigma }}_{1}^{1}$ choice and ${\mathrm{\Delta }}_{1}^{1}$ comprehension. We prove in this paper that ${\mathrm{\Sigma }}_{1}^{1}$ induction is needed for (...)
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  34. Two Applications of Finite Side Conditions at $$\Omega _2$$ Ω 2.Itay Neeman - forthcoming - Archive for Mathematical Logic.
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