36 found
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  1.  9
    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.  18
    Aronszajn Trees and Failure of the Singular Cardinal Hypothesis.Itay Neeman - 2009 - Journal of Mathematical Logic 9 (1):139-157.
    The tree property at κ+ states that there are no Aronszajn trees on κ+, or, equivalently, that every κ+ tree has a cofinal branch. For singular strong limit cardinals κ, there is tension between the tree property at κ+ and failure of the singular cardinal hypothesis at κ; the former is typically the result of the presence of strongly compact cardinals in the background, and the latter is impossible above strongly compacts. In this paper, we reconcile the two. We prove (...)
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  3.  8
    The Tree Property Up to אω+1.Itay Neeman - 2014 - Journal of Symbolic Logic 79 (2):429-459.
  4.  15
    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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  5.  44
    Optimal Proofs of Determinacy.Itay Neeman - 1995 - Bulletin of Symbolic Logic 1 (3):327-339.
  6.  8
    Happy and Mad Families in L.Itay Neeman & Zach Norwood - 2018 - Journal of Symbolic Logic 83 (2):572-597.
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  7.  28
    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. 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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  9.  5
    Chang’s Conjecture with $$square {omega _1, 2}$$□ω1,2 from an $$omega 1$$ω1 -Erdős cardinal.Itay Neeman & John Susice - forthcoming - Archive for Mathematical Logic:1-12.
    Answering a question of Sakai :29–45, 2013), we show that the existence of an \-Erdős cardinal suffices to obtain the consistency of Chang’s Conjecture with \. By a result of Donder, volume 872 of lecture notes in mathematics. Springer, Berlin, pp 55–97, 1981) this is best possible. We also give an answer to another question of Sakai relating to the incompatibility of \ and \ \twoheadrightarrow \) for uncountable \.
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  10.  13
    Two Applications of Finite Side Conditions at Omega _2.Itay Neeman - 2017 - Archive for Mathematical Logic 56 (7-8):983-1036.
    We present two applications of forcing with finite sequences of models as side conditions, adding objects of size \. The first involves adding a \ sequence and variants of such sequences. The second involves adding partial weak specializing functions for trees of height \.
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  11.  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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  12.  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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  13.  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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  14.  66
    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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  15.  15
    Optimal Proofs of Determinacy II.Itay Neeman - 2002 - Journal of Mathematical Logic 2 (2):227-258.
    We present a general lemma which allows proving determinacy from Woodin cardinals. The lemma can be used in many different settings. As a particular application we prove the determinacy of sets in [Formula: see text], n ≥ 1. The assumption we use to prove [Formula: see text] determinacy is optimal in the base theory of [Formula: see text] determinacy.
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  16.  13
    Square Principles with Tail-End Agreement.William Chen & Itay Neeman - 2015 - Archive for Mathematical Logic 54 (3-4):439-452.
    This paper investigates the principles □λ,δta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square^{{{\rm ta}}}_{\lambda,\delta}}$$\end{document}, weakenings of □λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square_\lambda}$$\end{document} which allow δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\delta}$$\end{document} many clubs at each level but require them to agree on a tail-end. First, we prove that □λ,<ωta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square^{{\rm {ta}}}_{\lambda,< \omega}}$$\end{document} implies □λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square_\lambda}$$\end{document}. Then, (...)
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  17.  60
    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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  18.  10
    The Strength of Jullien's Indecomposability Theorem.Itay Neeman - 2008 - Journal of Mathematical Logic 8 (1):93-119.
    Jullien's indecomposability theorem 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. We identify the strength of the theorem relative to standard reverse mathematics markers. We show that it lies strictly between weak [Formula: see text] choice and [Formula: see text] comprehension.
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  19.  15
    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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  20.  12
    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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  21.  53
    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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  22.  11
    William Mitchell, Ernest Schimmerling, and John Steel. The Covering Lemma Up to a Woodin Cardinal. Annals of Pure and Applied Logic, Vol. 84 , Pp. 219–255. [REVIEW]Itay Neeman - 2003 - Bulletin of Symbolic Logic 9 (3):414-416.
  23.  18
    Proper Forcings and Absoluteness in LProper Forcing and L.Paul B. Larson, Itay Neeman & Jindrich Zapletal - 2002 - Bulletin of Symbolic Logic 8 (4):548.
  24.  14
    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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  25.  17
    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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  26.  11
    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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  27.  15
    Annals of Pure and Applied Logic.Itay Neeman - 2003 - Bulletin of Symbolic Logic 9 (3):414-416.
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  28.  16
    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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  29.  15
    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.
  30.  10
    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.
  31.  13
    Effective Cardinals of Boldface Pointclasses.Alessandro Andretta, Greg Hjorth & Itay Neeman - 2007 - Journal of Mathematical Logic 7 (1):35-82.
    Assuming AD + DC, we characterize the self-dual boldface pointclasses which are strictly larger than the pointclasses contained in them: these are exactly the clopen sets, the collections of all sets of Wadge rank [Formula: see text], and those of Wadge rank [Formula: see text] when ξ is limit.
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  32.  7
    2011 North American Annual Meeting of the Association for Symbolic Logic.Itay Neeman - 2012 - Bulletin of Symbolic Logic 18 (2):275-305.
  33.  6
    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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  34.  7
    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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  35.  5
    Games of Length Ω1.Itay Neeman - 2007 - Journal of Mathematical Logic 7 (1):83-124.
    We prove determinacy for open length ω1 games. Going further we introduce, and prove determinacy for, a stronger class of games of length ω1, with payoff conditions involving the entire run, the club filter on ω1, and a sequence of ω1 disjoint stationary subsets of ω1. The determinacy proofs use an iterable model with a class of indiscernible Woodin cardinals, and we show that the games precisely capture the theory of the minimal model for this assumption.
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  36. Chang’s Conjecture with $$\Square {\Omega _1, 2}$$ From an $$\Omega 1$$-Erdős Cardinal.Itay Neeman & John Susice - forthcoming - Archive for Mathematical Logic.
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