منابع مشابه
Level Compactness
The concept of compactness is a necessary condition of any system that is going to call itself a finitary method of proof. However, it can also apply to predicates of sets of formulas in general and in that manner it can be used in relation to level functions, a flavor of measure functions. In what follows we will tie these concepts of measure and compactness together and expand some concepts w...
متن کاملLevel by Level Inequivalence , Strong Compactness , and GCH ∗ † Arthur
We construct three models containing exactly one supercompact cardinal in which level by level inequivalence between strong compactness and supercompactness holds. In the first two models, below the supercompact cardinal κ, there is a non-supercompact strongly compact cardinal. In the last model, any suitably defined ground model Easton function is realized.
متن کاملIndestructibility, instances of strong compactness, and level by level inequivalence
Suppose λ > κ is measurable. We show that if κ is either indestructibly supercompact or indestructibly strong, then A = {δ < κ | δ is measurable, yet δ is neither δ+ strongly compact nor a limit of measurable cardinals} must be unbounded in κ. The large cardinal hypothesis on λ is necessary, as we further demonstrate by constructing via forcing two models in which A = ∅. The first of these cont...
متن کاملIndestructibility, Strong Compactness, and Level by Level Equivalence
We show the relative consistency of the existence of two strongly compact cardinals κ1 and κ2 which exhibit indestructibility properties for their strong compactness, together with level by level equivalence between strong compactness and supercompactness holding at all measurable cardinals except for κ1. In the model constructed, κ1’s strong compactness is indestructible under arbitrary κ1-dir...
متن کاملIndestructible Strong Compactness and Level by Level Equivalence with No Large Cardinal Restrictions
We construct a model for the level by level equivalence between strong compactness and supercompactness with an arbitrary large cardinal structure in which the least supercompact cardinal κ has its strong compactness indestructible under κ-directed closed forcing. This is in analogy to and generalizes [3, Theorem 1], but without the restriction that no cardinal is supercompact up to an inaccess...
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ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 2006
ISSN: 0029-4527
DOI: 10.1305/ndjfl/1168352667