منابع مشابه
Collapsing Successors of Singulars
Let κ be a singular cardinal in V , and let W ⊇ V be a model such that κ+V = λ + W for some W -cardinal λ with W |= cf(κ) 6= cf(λ). We apply Shelah’s pcf theory to study this situation, and prove the following results. 1) W is not a κ+-c.c generic extension of V . 2) There is no “good scale for κ” in V , so in particular weak forms of square must fail at κ. 3) If V |= cf(κ) = א0 then V |= “κ is...
متن کاملSuccessor of Singulars: Combinatorics and Not Collapsing Cardinals
On the one hand we deal with (< κ)-supported iterated forcing notions which are (Ê0, Ê1)-complete, have in mind problems on Whitehead groups, uniformizations and the general problem. We deal mainly with the caes of a successor of the singular cardinal. This continues [Sh 587]. On the other hand we deal with complimentary ZFC combinatorial results. I would like to thank Alice Leonhardt for the b...
متن کاملSaturated Filters at Successors of Singulars, Weak Reflection and Yet Another Weak Club Principle
Suppose that λ is the successor of a singular cardinal μ whose cofinality is an uncountable cardinal κ. We give a sufficient condition that the club filter of λ concentrating on the points of cofinality κ is not λ-saturated. The condition is phrased in terms of a notion that we call weak reflection. We discuss various properties of weak reflection. We introduce a weak version of the ♣-principle...
متن کاملOn the Generic Use of Indefinite Singulars
The distribution of indefinite singular generics is much more restricted than that of bare plural generics. The former, unlike the latter, seem to require that the property predicated of their subject be, in some sense, “definitional”. Moreover, the two constructions exhibit different scopal behavior, and differ in their felicity in conjunctions, questions, and expressions describing the speake...
متن کاملOn successors of Jónsson cardinals
We show that, like singular cardinals, and weakly compact cardinals, Jensen's core model K for measures of order zero 4] calculates correctly the successors of JJ onsson cardinals, assuming O Sword does not exist. Namely, if is a JJ onsson cardinal then + = +K , provided that there is no non-trivial elementary embedding j : K ?! K. There are a number of related results in ZF C concerning P() in...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1997
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-97-03995-6