1998 European Summer Meeting of the Association for Symbolic by PDF


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Math. princeton. edu/-nelson). PATRICK BELLOT, Imperative program synthesis using a logic of actions. Ecole Nationale SupCrieure des Telecommunications, Computer Science Department, Software Engineering group, 46 rue Barrault, 75634 Paris Cedex 13, France. e n s t . f r. Program synthesis using logic usually produces functional programs, that is I-expressions which do only computations on data represented by abstract data types. This is due to the purely mathematical nature of these systems. But computer programming does not deal with mathematical objects but with real data implementation, real objects such as disk files and pre-existing programs.

Mathematics Department, Caltech, Pasadena. CA 91 125. E-mail: kechrisBcaltech. edu. In this talk I will discuss recent results and open problems concerning the structure of Borel equivalence relations on Polish spaces. PAVOL ZLATOS, Indiscernibles in the alternative set theory. Mathematics Department, Comenius University, Mlynska dolina, 84215 Bratislava, Slovak Republic. sk. The alternative set theory (AST), developed by P. VopCnka, aims to provide an alternative to the classical Cantor's set theory in the foundations of mathematics.

We take a topological structure to be a transition system 6 = ( X , 7 , { $ ) a t ~ c t , A ) ,additionally equipped with a topology I on X and a valuation algebra A: a Boolean algebra of subsets of X containing 7 and closed under each r,. The range of atomic assignments 4 for 6 is restricted to A. Then -f: is upper- (lower-) semi-continuous with respect to I if and only if the schema [a]Ocp -+ O[a]cp ( ( a ) @ -+ O(a)cp) is valid in 6. Let TAL be the logic obtained from TALo by adding the two continuity axiom schemes for each a E Act.

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1998 European Summer Meeting of the Association for Symbolic Logic. Logic Colloquium '98

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