A model M of cardinality λ is said to have the small index property if for every G ⊆ Aut(M) such that [Aut(M) : G] ≤ λ there is an A ⊆ M with ∣

We present in this paper a peptide matching approach to the multiple comparison of a set of protein sequences. This approach consists in looking for all the words that are common to q of these sequences, where q is a parameter. The comparison between words is done by using as reference an object called a model. In the case of proteins, a model is a product of subsets of the alphabet Σ of the am...

Blass, A. and A. Scedrov, Complete topoi representing models of set theory, Annals of Pure and Applied Logic 57 (1992) l-26. By a model of set theory we mean a Boolean-valued model of Zermelo-Fraenkel set theory allowing atoms (ZFA), which contains a copy of the ordinary universe of (two-valued, pure) sets as a transitive subclass; examples include Scott-Solovay Boolean-valued models and their ...

In this paper we prove that if κ is a cardinal in L[0], then there is an inner model M such that M |= (Vκ,∈) has no elementary end extension. In particular if 0♯ exists then weak compactness is never downwards absolute. We complement the result with a lemma stating that any cardinal greater than א1 of uncountable cofinality in L[0♯] is Mahlo in every strict inner model of L[0♯].