European Summer Meeting of the Association for Symbolic Logic: Aachen, 1983

S OF PAPERS 261 R. BONNET, Sur les algebres de Boole d'intervalles. Rappelons qu'historiquement, les algebres de Boole interviennent en logique (Lindenbaum-Tarski), theorie de la mesure, et plus recemment en theorie des ensembles et en topologie. Dans cet article, on va exposer quelques aspects relatifs aux algebres de Boole d'intervalles. On commence (?0) par expliciter la duality "algebres de Boole-espaces Booleiens" (M. Pouzet, voir aussi Ch. Charretton et M. Pouzet); il est a noter que l'espace est "concret" et que l'on n'utilise pas l'axiome de l'ultrafiltre et donc pas l'axiome du choix. Le ?1 sera consacre aux algebres de Boole denombrables (theoremes de Mostowski-Tarski; Mayer-Pierce, Ketonen) et un resultat (non encore public) concernant le theoreme de Tarski sur l'equivalence elementaire, dans le cas des algebres denombrables. Enfin dans le ?2, on developpera les algebres retractives (Rubin), les types d'isomorphie (en utilisant les idees de Shelah) et les algebres rigides. BRANISLAV R. BORICIC, On an intermediate propositional system. By giving a positive solution to the problem posed in [6] we have shown (v. [1]) that the sequence of intermediate propositional systems NLCn (n ? 1) contains three different systems only: the classical propositional calculus NLC1, Dummett's system NLC2 (v. [3]) and the system NLC3. We will consider the completeness, separability and decidability of the last system. Note that NLC3 can be axiomatized by adding the formula C3: ((A -* B) -* D) -*(((B -* C) -* D) (((C A) D) D)) as an axiom to the Heyting propositional calculus H. IH + C3 is the positive implicational calculus (v. [2]) extended by C3. THEOREM 1. IH + C3 is characterised by all Kripke frames (X, R) (i.e. partially ordered sets) with the

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