منابع مشابه
Traditions and True Successors
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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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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...
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Extensions of the two variable fragment of FO (henceforth denoted as FO) with interpreted predicates have been of interest recently in the context of verification of infinite state systems and semi-structured data (in particular XML). We briefly discuss one specific problem, namely FO over datawords. Datawords are linear orders (denoted by ≺ where ≺ denotes the successor relation) labelled by a...
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The questions concerning existence of Aronszajn and Souslin trees are of the oldest and most dealt-with in modern set theory. There are many results about existence of h+-Aronszajn trees for regular cardinals A. For these cases the answer is quite complete. (See Jech [6] and Kanamory & Magidor [8] for details.) The situation is quite different when A is a singular cardinal. There are very few r...
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ژورنال
عنوان ژورنال: Nexus Network Journal
سال: 2008
ISSN: 1590-5896,1522-4600
DOI: 10.1007/s00004-007-0059-5