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...

BACKGROUND The existence of double primary teeth associated with further problems in permanent successors may have deleterious effects on occlusion and esthetics. The purposes of this study were to investigate the prevalence of double teeth in a group of Taiwanese children under 17 years old, and to compare the distribution of the different types of double primary teeth and their relationship t...

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...