Saharon Shelah

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We prove that the three extensions of first-order logic by means of positive inductions, monotone inductions, and so-called non-monotone (in our terminology, inflationary) inductions respectively, all have the same expressive power in the case of finite structures. As a by-product, the collapse of the corresponding fixed-point hierarchies can be deduced.
The formalism of temporal Logic has been suggested as a most appropriate tool, for reasoning about programs and their Originally, temporal Logic has been designed in order to analyze and reason about time sequences in general. Formalizing the possible variations in time of a varying (dynamic) situation, we consider time sequences s0, s1, . . . , where each(More)
Motivated by the minimal tower problem, an earlier work studied diagonalizations of covers where the covers are related to linear quasiorders (τ -covers). We deal with two types of combinatorial questions which arise from this study. 1. Two new cardinals introduced in the topological study are expressed in terms of well known cardinals characteristics of(More)
Turing machines define polynomial time (PTime) on strings but cannot deal with structures like graphs directly, and there is no known, easily computable string encoding of isomorphism classes of structures. Is there a computation model whose machines do not distinguish between isomorphic structures and compute exactly PTime properties? This question can be(More)
We apply model theoretic methods to the problem of existence of countable universal graphs with finitely many forbidden connected subgraphs. We show that to a large extent the question reduces to one of local finiteness of an associated “algebraic closure” operator (Theorem 3, §3). The main applications are new examples of universal graphs with forbidden(More)