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  1. Itay Neeman (2014). Forcing with Sequences of Models of Two Types. 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. Itay Neeman (2012). 2011 North American Annual Meeting of the Association for Symbolic Logic. Bulletin of Symbolic Logic 18 (2).
     
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  3. Itay Neeman (2011). Necessary Use of [Image] Induction in a Reversal. 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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  4. Gunter Fuchs, Itay Neeman & Ralf Schindler (2010). A Criterion for Coarse Iterability. 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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  5. Itay Neeman (2009). Aronszajn Trees and Failure of the Singular Cardinal Hypothesis. Journal of Mathematical Logic 9 (01):139-157.
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  6. Itay Neeman (2008). Finite State Automata and Monadic Definability of Singular Cardinals. 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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  7. Itay Neeman (2008). Hierarchies of Forcing Axioms II. 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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  8. Itay Neeman (2008). The Strength of Jullien's Indecomposability Theorem. Journal of Mathematical Logic 8 (01):93-119.
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  9. Itay Neeman & Ernest Schimmerling (2008). Hierarchies of Forcing Axioms I. 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. Alessandro Andretta, Greg Hjorth & Itay Neeman (2007). Effective Cardinals of Boldface Pointclasses. Journal of Mathematical Logic 7 (01):35-82.
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  11. Moti Gitik, Itay Neeman & Dima Sinapova (2007). A Cardinal Preserving Extension Making the Set of Points of Countable V Cofinality Nonstationary. 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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  12. Itay Neeman (2007). Games of Length Ω1. Journal of Mathematical Logic 7 (01):83-124.
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  13. Itay Neeman (2007). Inner Models and Ultrafilters in L(R). 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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  14. Douglas Cenzer, C. Ward Henson, Michael C. Laskowski, Alain Louveau, Russell Miller, Itay Neeman, Sergei Starchenko & Valentina Harizanov (2006). San Antonio Convention Center San Antonio, Texas January 14–15, 2006. Bulletin of Symbolic Logic 12 (4).
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  15. Itay Neeman (2006). Determinacy for Games Ending at the First Admissible Relative to the Play. 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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  16. Itay Neeman & John Steel (2006). Counterexamples to the Unique and Cofinal Branches Hypotheses. 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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  17. Itay Neeman (2004). The Mitchell Order Below Rank-To-Rank. 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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  18. Donald A. Martin, Itay Neeman & Marco Vervoort (2003). The Strength of Blackwell Determinacy. 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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  19. W. Mitchell, E. Schimmerling, J. Steel & Itay Neeman (2003). REVIEWS-The Covering Lemma Up to a Woodin Cardinal. Bulletin of Symbolic Logic 9 (3):414-416.
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  20. Itay Neeman (2003). 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] Bulletin of Symbolic Logic 9 (3):414-416.
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  21. Itay Neeman (2002). Inner Models in the Region of a Woodin Limit of Woodin Cardinals. Annals of Pure and Applied Logic 116 (1-3):67-155.
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  22. Itay Neeman (2002). Optimal Proofs of Determinacy II. Journal of Mathematical Logic 2 (02):227-258.
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  23. Itay Neeman, Alexander Leitsch, Toshiyasu Arai, Steve Awodey, James Cummings, Rod Downey & Harvey Friedman (2002). 2001 European Summer Meeting of the Association for Symbolic Logic Logic Colloquium'01. Bulletin of Symbolic Logic 8 (1).
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  24. Itay Neeman & Jindřich Zapletal (2001). Proper Forcing and L(ℝ). 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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  25. Itay Neeman (2000). Unraveling Sets. Annals of Pure and Applied Logic 106 (1-3):151-205.
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  26. Itay Neeman (2000). Unraveling Π11 Sets. Annals of Pure and Applied Logic 106 (1):151-205.
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  27. Itay Neeman & John Steel (1999). A Weak Dodd-Jensen Lemma. 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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  28. Tomek Bartoszynski, Harvey Friedman, Geoffrey Hellman, Bakhadyr Khoussainov, Phokion G. Kolaitis, Richard Shore, Charles Steinhorn, Mirna Dzamonja, Itay Neeman & Slawomir Solecki (1996). 1995–1996 Annual Meeting of the Association for Symbolic Logic. Bulletin of Symbolic Logic 2 (4).
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  29. Itay Neeman (1995). Optimal Proofs of Determinacy. Bulletin of Symbolic Logic 1 (3):327-339.
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