Model theory and arithmetic (Lecture Notes in Mathematics 890)

Description

Depuis les annees soixante-dix, on assiste a un renouveau de 1 'etude des systemes axiomatiques de 1 ' Ar ithmetique, notamment par les methodes semantiques de la theorie des modeles. Ce recueil de textes t&moigne de la variete des techniques appliquees actuellement et des themes abordes. 11 est le fruit d'une Action Thematique Programmee du C.N.R.S. , qui s'est deroulee en 1979-1980 dans le Laboratoi- re de Theories Geometriques, Laboratoire de 1'Universite Paris VII, associe au Centre National de la Recherche Scientifique.

Cette A.T.P. s'est structuree autour d'un seminaire et de divers groupes de travail et a accueilli de nombreux participants. Les textes qui suivent sont bases sur le travail et les exposes faits a cette occasion. Nous avons place en tete les 2 articles qui fournissent une introduction au sujet ; les autres textes sont presen- tes par ordre alphabetique des auteurs, solution retenue vu la diversite des contributions.

Nous tenons a remercier Mile M.T. Gschwendtner et son equipe administrative a l'U.B.R. de mathematiques de l'Universite Paris VII, specialement Mmes 3. Arpin et C. Pradier, qui ont assure avec soin la dactylographie, et Mile C. Valentin sur qui reposait la reproduction et diffusion reguliere des documents de l'A.T.P.

Contents:
Anand PILLAY Models of Peano Arithmetic (a survey of basic results) 1
Anand PILLAY Cuts in Models of Arithmetic 13
Peter ACZEL Two notes on the Paris independence result 21
Chantal BERLINE Ideaux des anneaux de Peano (d'apres CHERLIN) 32
Patrick CEGIELSKI Theorie elementaire de la multiplication des entiers naturels 44
Zoe CHATZIDAKIS La representation en termes de faisceaux des modeles de la theorie elementaire de la multiplication des entiers naturels 90
Greg L. CHERLIN, Max A. DICKMANN Note on a Nullstellensatz 111
Peter CLOTE Anti-Basis theorems and their relation to independence results in Peano ari thmeti c 115
Peter CLOTE A note on Decidable Model theory 134
Michele JAMBU-GIRAUDET Interpretations d'Arithmetiques dans des groupes et des treillis 143
Kenneth Mc ALOON, Jean-Pierre RESSAYRE Les methodes de KIRBY-PARIS et la theorie des ensembles 154
Angus MACINTYRE The laws of exponentiation 185
M. MARGENSTERN Le theoreme de MATIYASSEVITCH et resultats connexes 198
Pascal MICHEL Borne superieure de la complexite de IN muni de la relation de divisibilite 242
Jeff B. PARIS Some conservation results for fragments of arithmetic 251
Anand PILLAY Partition properties and definable types in Peano Arithmetic 263
Denis RICHARD De la structure additive a la saturation des modeles de Pe'ano et a une classification des sous-langages de 1 'Arithmetique 270
Alex J. WILKIE On discretely ordered rings in which every definable ideal is principal 297
George WILMERS An observation concerning the relationship between finite and infinitary resentences 304

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