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  1. Moti Gitik (2013). A Model with a Precipitous Ideal, but No Normal Precipitous Ideal. Journal of Mathematical Logic 13 (1):1250008.
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  2. Moti Gitik & Saharon Shelah (2013). Applications of Pcf for Mild Large Cardinals to Elementary Embeddings. Annals of Pure and Applied Logic 164 (9):855-865.
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  3. Arthur W. Apter, Moti Gitik & Grigor Sargsyan (2012). Indestructible Strong Compactness but Not Supercompactness. Annals of Pure and Applied Logic 163 (9):1237-1242.
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  4. Eilon Bilinsky & Moti Gitik (2012). A Model with a Measurable Which Does Not Carry a Normal Measure. Archive for Mathematical Logic 51 (7-8):863-876.
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  5. Moti Gitik (2012). Short Extenders Forcings I. Journal of Mathematical Logic 12 (2):1250009.
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  6. Moti Gitik & Liad Tal (2011). On the Strength of No Normal Precipitous Filter. Archive for Mathematical Logic 50 (1-2):223-243.
    We consider a question of T. Jech and K. Prikry that asks if the existence of a precipitous filter implies the existence of a normal precipitous filter. The aim of this paper is to improve a result of Gitik (Israel J Math, 175:191–219, 2010) and to show that measurable cardinals of a higher order rather than just measurable cardinals are necessary in order to have a model with a precipitous filter but without a normal one.
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  7. Asaf Ferber & Moti Gitik (2010). On Almost Precipitous Ideals. Archive for Mathematical Logic 49 (3):301-328.
    With less than 0# two generic extensions ofL are identified: one in which ${\aleph_1}$ , and the other ${\aleph_2}$ , is almost precipitous. This improves the consistency strength upper bound of almost precipitousness obtained in Gitik M, Magidor M (On partialy wellfounded generic ultrapowers, in Pillars of Computer Science, 2010), and answers some questions raised there. Also, main results of Gitik (On normal precipitous ideals, 2010), are generalized—assumptions on precipitousness are replaced by those on ∞-semi precipitousness. As an application it (...)
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  8. Moti Gitik (2010). On Changing Cofinality of Partially Ordered Sets. Journal of Symbolic Logic 75 (2):641-660.
    It is shown that under GCH every poset preserves its confinality in any cofinality preserving extension. On the other hand, starting with ω measurable cardinals, a model with a partial ordered set which can change its cofinality in a cofinality preserving extension is constructed.
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  9. Moti Gitik & John Krueger (2009). Approachability at the Second Successor of a Singular Cardinal. Journal of Symbolic Logic 74 (4):1211 - 1224.
    We prove that if μ is a regular cardinal and ℙ is a μ-centered forcing poset, then ℙ forces that $(I[\mu ^{ + + } ])^V $ generates I[µ⁺⁺] modulo clubs. Using this result, we construct models in which the approachability property fails at the successor of a singular cardinal. We also construct models in which the properties of being internally club and internally approachable are distinct for sets of size the successor of a singular cardinal.
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  10. Moti Gitik (2008). On a Question of Pereira. Archive for Mathematical Logic 47 (1):53-64.
    Answering a question of Pereira we show that it is possible to have a model violating the Singular Cardinal Hypothesis without a tree-like continuous scale.
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  11. Moti Gitik (2008). Some Pathological Examples of Precipitous Ideals. Journal of Symbolic Logic 73 (2):492 - 511.
    We construct a model with an indecisive precipitous ideal and a model with a precipitous ideal with a non precipitous normal ideal below it. Such kind of examples were previously given by M. Foreman [2] and R. Laver [4] respectively. The present examples differ in two ways: first- they use only a measurable cardinal and second- the ideals are over a cardinal. Also a precipitous ideal without a normal ideal below it is constructed. It is shown in addition that if (...)
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  12. 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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  13. Moti Gitik & Carmi Merimovich (2006). Power Function on Stationary Classes. Annals of Pure and Applied Logic 140 (1):75-103.
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  14. Moti Gitik (2005). No Bound for the First Fixed Point. Journal of Mathematical Logic 5 (02):193-246.
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  15. Moti Gitik (2005). Around Silver's Theorem. Notre Dame Journal of Formal Logic 46 (3):323-325.
    We state some results related to the Silver Theorem.
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  16. Moti Gitik & Akihiro Kanamori (2003). REVIEWS-Moti Gitik's Recent Papers on the Singular Cardinals Problem. Bulletin of Symbolic Logic 9 (2):237-241.
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  17. Moti Gitik (2002). Blowing Up Power of a Singular Cardinal—Wider Gaps. Annals of Pure and Applied Logic 116 (1-3):1-38.
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  18. Moti Gitik & Saharon Shelah (2001). On Some Configurations Related to the Shelah Weak Hypothesis. Archive for Mathematical Logic 40 (8):639-650.
    We show that some cardinal arithmetic configurations related to the negation of the Shelah Weak Hypothesis and natural from the forcing point of view are impossible.
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  19. Moti Gitik (1999). On Closed Unbounded Sets Consisting of Former Regulars. Journal of Symbolic Logic 64 (1):1-12.
    A method of iteration of Prikry type forcing notions as well as a forcing for adding clubs is presented. It is applied to construct a model with a measurable cardinal containing a club of former regulars, starting with o(κ) = κ + 1. On the other hand, it is shown that the strength of above is at least o(κ) = κ.
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  20. Moti Gitik & Saharon Shelah (1999). Cardinal Preserving Ideals. Journal of Symbolic Logic 64 (4):1527-1551.
    We give some general criteria, when κ-complete forcing preserves largeness properties-like κ-presaturation of normal ideals on λ (even when they concentrate on small cofinalities). Then we quite accurately obtain the consistency strength "NS λ is ℵ 1 -preserving". for λ > ℵ 2.
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  21. Arthur W. Apter & Moti Gitik (1998). The Least Measurable Can Be Strongly Compact and Indestructible. Journal of Symbolic Logic 63 (4):1404-1412.
    We show the consistency, relative to a supercompact cardinal, of the least measurable cardinal being both strongly compact and fully Laver indestructible. We also show the consistency, relative to a supercompact cardinal, of the least strongly compact cardinal being somewhat supercompact yet not completely supercompact and having both its strong compactness and degree of supercompactness fully Laver indestructible.
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  22. Moti Gitik & Carmi Merimovich (1997). Possible Values for 2ℵn and 2ℵω. Annals of Pure and Applied Logic 90 (1-3):193-241.
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  23. Moti Gitik & Carmi Merimovich (1997). Possible Values for 2 (Aleph N) and 2 (Aleph Omega). Annals of Pure and Applied Logic 90 (1-3):193-241.
     
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  24. Moti Gitik & Carmi Merimovich (1997). Possible Values for 2< Sup> and 2. Annals of Pure and Applied Logic 90 (1):193-241.
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  25. Moti Gitik (1996). Blowing Up the Power of a Singular Cardinal. Annals of Pure and Applied Logic 80 (1):17-33.
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  26. Moti Gitik (1996). On Hidden Extenders. Archive for Mathematical Logic 35 (5-6):349-369.
    We prove the following theorem: Suppose that there is a singular $\kappa$ with the set of $\alpha$ 's with $o(\alpha)=\alpha^{+n}$ unbounded in it for every $n < \omega$ . Then in a generic extesion there are two precovering sets which disagree about common indiscernibles unboundedly often.
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  27. Moti Gitik & William J. Mitchell (1996). Indiscernible Sequences for Extenders, and the Singular Cardinal Hypothesis. Annals of Pure and Applied Logic 82 (3):273-316.
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  28. Sanjeev Arora, Matthias Baaz, Lenore Blum, Patrick Dehornoy, Solomon Feferman, Moti Gitik, Erich Grädel, Yuri Gurevich, Serge Grigorieff & David Harel (1995). Clermont-Ferrand, France, July 21–30, 1994. Bulletin of Symbolic Logic 1 (2).
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  29. Moti Gitik & Menachem Magidor (1994). Extender Based Forcings. Journal of Symbolic Logic 59 (2):445-460.
    The paper is a continuation of [The SCH revisited]. In § 1 we define a forcing with countably many nice systems. It is used, for example, to construct a model "GCH below κ, c f κ = ℵ0, and $2^\kappa > \kappa^{+\omega}$" from 0(κ) = κ+ω. In § 2 we define a triangle iteration and use it to construct a model satisfying "{μ ≤ λ∣ c f μ = ℵ0 and $pp(\mu) > \lambda\}$ is countable for some λ". The question (...)
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  30. Moti Gitik (1993). On Measurable Cardinals Violating the Continuum Hypothesis. Annals of Pure and Applied Logic 63 (3):227-240.
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  31. Moti Gitik (1991). The Strenght of the Failure of the Singular Cardinal Hypothesis. Annals of Pure and Applied Logic 51 (3):215-240.
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  32. Moti Gitik (1989). On Generic Elementary Embeddings. Journal of Symbolic Logic 54 (3):700-707.
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  33. Moti Gitik (1989). The Negation of the Singular Cardinal Hypothesis From o(K)=K++. Annals of Pure and Applied Logic 43 (3):209-234.
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  34. Moti Gitik (1989). The Negation of the Singular Cardinal Hypothesis From< I> o(< I> K_)=< I> K< Sup>++. Annals of Pure and Applied Logic 43 (3):209-234.
     
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  35. Moti Gitik & Saharon Shelah (1989). On Certain Indestructibility of Strong Cardinals and a Question of Hajnal. Archive for Mathematical Logic 28 (1):35-42.
    A model in which strongness ofκ is indestructible under κ+ -weakly closed forcing notions satisfying the Prikry condition is constructed. This is applied to solve a question of Hajnal on the number of elements of {λ δ |2 δ <λ}.
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  36. Moti Gitik (1988). On the Mitchell and Rudin-Kiesler Orderings of Ultrafilters. Annals of Pure and Applied Logic 39 (2):175-197.
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  37. Moti Gitik (1986). On Precipitousness of the Nonstationary Ideal Over a Supercompact. Journal of Symbolic Logic 51 (3):648-662.
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  38. Moti Gitik (1985). Nonsplitting Subset of Pκ(Κ+). Journal of Symbolic Logic 50 (4):881 - 894.
    Assuming the existence of a supercompact cardinal, we construct a model of ZFC + (There exists a nonsplitting stationary subset of P | kappa(κ +) ). Answering a question of Uri Abraham [A], [A-S], we prove that adding a real to the world always makes P ℵ 1 (ℵ 2 ) - V stationary.
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  39. Moti Gitik (1985). Nonsplitting Subset of $Mathscr{P}_kappa(Kappa^+)$. Journal of Symbolic Logic 50 (4):881-894.
    Assuming the existence of a supercompact cardinal, we construct a model of ZFC + (There exists a nonsplitting stationary subset of $\mathscr{P}_|kappa(\kappa^+)$). Answering a question of Uri Abraham [A], [A-S], we prove that adding a real to the world always makes $\mathscr{P}_{\aleph_1}(\aleph_2) - V$ stationary.
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  40. Moti Gitik (1981). On Non-Minimal P-Points Over a Measurable Cardinal. Annals of Mathematical Logic 20 (3):269-288.
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