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  1. Indiscernible Sequences for Extenders, and the Singular Cardinal Hypothesis.Moti Gitik & William J. Mitchell - 1996 - Annals of Pure and Applied Logic 82 (3):273-316.
    We prove several results giving lower bounds for the large cardinal strength of a failure of the singular cardinal hypothesis. The main result is the following theorem: Theorem. Suppose κ is a singular strong limit cardinal and 2κ λ where λ is not the successor of a cardinal of cofinality at most κ. If cf > ω then it follows that o λ, and if cf = ωthen either o λ or {α: K o α+n} is confinal in κ for (...)
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  • Possible Values for 2ℵn and 2ℵω.Moti Gitik & Carmi Merimovich - 1997 - Annals of Pure and Applied Logic 90 (1-3):193-241.
  • On Gaps Under GCH Type Assumptions.Moti Gitik - 2003 - Annals of Pure and Applied Logic 119 (1-3):1-18.
    We prove equiconsistency results concerning gaps between a singular strong limit cardinal κ of cofinality 0 and its power under assumptions that 2κ=κ+δ+1 for δ<κ and some weak form of the Singular Cardinal Hypothesis below κ. Together with the previous results this basically completes the study of consistency strength of the various gaps between such κ and its power under GCH type assumptions below.
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  • The Strenght of the Failure of the Singular Cardinal Hypothesis.Moti Gitik - 1991 - Annals of Pure and Applied Logic 51 (3):215-240.
    We show that o = k++ is necessary for ¬SCH. Together with previous results it provides the exact strenght of ¬SCH.
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  • Changing Cardinal Characteristics Without Changing Ω-Sequences or Cofinalities.Heike Mildenberger & Saharon Shelah - 2000 - Annals of Pure and Applied Logic 106 (1-3):207-261.
    We show: There are pairs of universes V1V2 and there is a notion of forcing PV1 such that the change mentioned in the title occurs when going from V1[G] to V2[G] for a P-generic filter G over V2. We use forcing iterations with partial memories. Moreover, we implement highly transitive automorphism groups into the forcing orders.
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  • Global Singularization and the Failure of SCH.Radek Honzik - 2010 - Annals of Pure and Applied Logic 161 (7):895-915.
    We say that κ is μ-hypermeasurable for a cardinal μ≥κ+ if there is an embedding j:V→M with critical point κ such that HV is included in M and j>μ. Such a j is called a witnessing embedding.Building on the results in [7], we will show that if V satisfies GCH and F is an Easton function from the regular cardinals into cardinals satisfying some mild restrictions, then there exists a cardinal-preserving forcing extension V* where F is realised on all V-regular (...)
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  • A Laver-Like Indestructibility for Hypermeasurable Cardinals.Radek Honzik - forthcoming - Archive for Mathematical Logic:1-13.
    We show that if \ is \\)-hypermeasurable for some cardinal \ with \ \le \mu \) and GCH holds, then we can extend the universe by a cofinality-preserving forcing to obtain a model \ in which the \\)-hypermeasurability of \ is indestructible by the Cohen forcing at \ of any length up to \ is \\)-hypermeasurable in \). The preservation of hypermeasurability is useful for subsequent arguments. The construction of \ is based on the ideas of Woodin and Cummings :1–39, (...)
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  • The Failure of GCH at a Degree of Supercompactness.Brent Cody - 2012 - Mathematical Logic Quarterly 58 (1):83-94.
    We determine the large cardinal consistency strength of the existence of a λ-supercompact cardinal κ such that equation image fails at λ. Indeed, we show that the existence of a λ-supercompact cardinal κ such that 2λ ≥ θ is equiconsistent with the existence of a λ-supercompact cardinal that is also θ-tall. We also prove some basic facts about the large cardinal notion of tallness with closure.
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  • Eastonʼs Theorem and Large Cardinals From the Optimal Hypothesis.Sy-David Friedman & Radek Honzik - 2012 - Annals of Pure and Applied Logic 163 (12):1738-1747.
    The equiconsistency of a measurable cardinal with Mitchell order o=κ++ with a measurable cardinal such that 2κ=κ++ follows from the results by W. Mitchell [13] and M. Gitik [7]. These results were later generalized to measurable cardinals with 2κ larger than κ++ .In Friedman and Honzik [5], we formulated and proved Eastonʼs theorem [4] in a large cardinal setting, using slightly stronger hypotheses than the lower bounds identified by Mitchell and Gitik , for a suitable μ, instead of the cardinals (...)
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  • On Measurable Cardinals Violating the Continuum Hypothesis.Moti Gitik - 1993 - Annals of Pure and Applied Logic 63 (3):227-240.
    Gitik, M., On measurable cardinals violating the continuum hypothesis, Annals of Pure and Applied Logic 63 227-240. It is shown that an extender used uncountably many times in an iteration is reconstructible. This together with the Weak Covering Lemma is used to show that the assumption o=κ+α is necessary for a measurable κ with 2κ=κ+α.
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  • Forcing the Least Measurable to Violate GCH.Arthur W. Apter - 1999 - Mathematical Logic Quarterly 45 (4):551-560.
    Starting with a model for “GCH + k is k+ supercompact”, we force and construct a model for “k is the least measurable cardinal + 2k = K+”. This model has the property that forcing over it with Add preserves the fact k is the least measurable cardinal.
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  • Easton’s Theorem and Large Cardinals.Sy-David Friedman & Radek Honzik - 2008 - Annals of Pure and Applied Logic 154 (3):191-208.
    The continuum function αmaps to2α on regular cardinals is known to have great freedom. Let us say that F is an Easton function iff for regular cardinals α and β, image and α<β→F≤F. The classic example of an Easton function is the continuum function αmaps to2α on regular cardinals. If GCH holds then any Easton function is the continuum function on regular cardinals of some cofinality-preserving extension V[G]; we say that F is realised in V[G]. However if we also wish (...)
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  • Power Function on Stationary Classes.Moti Gitik & Carmi Merimovich - 2006 - Annals of Pure and Applied Logic 140 (1):75-103.
    We show that under certain large cardinal requirements there is a generic extension in which the power function behaves differently on different stationary classes. We achieve this by doing an Easton support iteration of the Radin on extenders forcing.
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  • A Model with a Precipitous Ideal, but No Normal Precipitous Ideal.Moti Gitik - 2013 - Journal of Mathematical Logic 13 (1):1250008.
  • Tall Cardinals.Joel D. Hamkins - 2009 - Mathematical Logic Quarterly 55 (1):68-86.
    A cardinal κ is tall if for every ordinal θ there is an embedding j: V → M with critical point κ such that j > θ and Mκ ⊆ M. Every strong cardinal is tall and every strongly compact cardinal is tall, but measurable cardinals are not necessarily tall. It is relatively consistent, however, that the least measurable cardinal is tall. Nevertheless, the existence of a tall cardinal is equiconsistent with the existence of a strong cardinal. Any tall cardinal (...)
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