منابع مشابه
Strong tree properties for two successive cardinals
An inaccessible cardinal κ is supercompact when (κ, λ)-ITP holds for all λ ≥ κ. We prove that if there is a model of ZFC with two supercompact cardinals, then there is a model of ZFC where simultaneously (א2, μ)-ITP and (א3, μ′)-ITP hold, for all μ ≥ א2 and μ′ ≥ א3.
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We construct a model in which for all 1 ≤ n < ω, there is no stationary subset of אn+1 ∩ cof(אn) which carries a partial square. Let κ be an uncountable cardinal and let μ ≤ κ be regular. A set A ⊆ κ∩cof(μ) is said to carry a partial square if there exists a sequence ⟨cα : α ∈ A⟩ such that each cα is club in α with order type μ, and for all γ which is a common limit point of cα and cβ , cα ∩ γ ...
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This paper is a survey of basic large cardinal notions, and applications of large cardinal ultrafilters in forcing. The main application presented is the consistent failure of the singular cardinals hypothesis. Other applications are mentioned that involve variants of Prikry forcing, over models of choice and models of determinacy. My talk at the Ultramath conference was about ultrafilters and ...
متن کاملCondensation and Large Cardinals
We introduce two generalized condensation principles: Local Club Condensation and Stationary Condensation. We show that while Strong Condensation (a generalized Condensation principle introduced by Hugh Woodin in [19]) is inconsistent with an ω1-Erdős cardinal, Stationary Condensation and Local Club Condensation (which should be thought of as weakenings of Strong Condensation) are both consiste...
متن کاملLarge Cardinals with Forcing
This chapter describes, following the historical development, the investigation of large cardinal hypotheses using the method of forcing. Large cardinal hypotheses, also regarded as strong axioms of infinity, have stimulated a vast mainstream of modern set theory, and William Mitchell’s chapter in this volume deals with their investigation through inner models, Menachem Kojman’s chapter with th...
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ژورنال
عنوان ژورنال: Annals of Mathematical Logic
سال: 1978
ISSN: 0003-4843
DOI: 10.1016/0003-4843(78)90019-0