Obiettivo Weak arithmetic is the study of problems of Number theory and Computer Science using methods of mathematical logic; just as Algebraic Number Theory or Analytic Number Theory use Algebra and Analysis. Five of the main sources of results in wreaks arithmetic's are undecidability of the field of rational numbers, Matiyasevich-Davis-Robinson-Putnam theorem, solving Hilbert's tenth problem, Erdös-Woods conjecture, Buss arithmetic and study of the real exponential field.The proposed project is constituted of nine teams from university of Paris, Steklov Institute of Mathematics at Saint-Petersburg (Russia), Udmurt University (Russia), Institute for Informatics and Automaton Problems at Yerevan (Armenia), Kiev University (Ukraine), University of Naples (Italy), university of Mons-Hainaut (Belgium), university of Clermont-Ferrand (France), and University of Athens (Greece).Objectives for the three years were :to construct Nonstandard Models of Buss Arithmetic to establish some bounds on the class NP inter co-NP ;to solve the problem of existence of end extensions of countable models of bounded collection ;to explore further the additive theory of infinite sets of prime numbers, both with absolute results and its links with number theory via the Schinzel's hypothesis ;to code natural numbers, complex numbers, and quadratic integers by automata accepting numbers (written in non-classical systems) ;to prove results for ultra-linear unary recursive schemata (with individual constants);to obtain decidability results for S2S[P] theories ;to build formal constructive theories with (from Grzegorczyk hierarchy) with applications to databases ;to investigate the power of counting in very small complexity classes and in the corresponding logical or arithmetical settings ;to explore the relation between Infinite games, automata, and arithmetic ;to study the fine structure of the BSS recursive enumerable sets ;to investigate concurrent processes in distributed conveyer systems and their relation with corresponding weak arithmetics;to construct Diophantine representations of recursively enumerable sets of particular interest ;to show the cofinality of primes in D0 (P), where P is the function which counts the primes below x ;to study subsystems of Goodstein's Arithmetic (without quantifiers) ;to develop families of formalized languages for presenting arithmetical texts.Main exchanges are by e-mail but it is planning two workshops (a local one and a general) by year, two co-ordination meeting and exchanges of scientists. Programma(i) IC-INTAS - International Association for the promotion of cooperation with scientists from the independent states of the former Soviet Union (INTAS), 1993- Argomento(i) 2 - Mathematics, Telecommunications, Information Technologies OPEN - OPEN Call Invito a presentare proposte Data not available Meccanismo di finanziamento Data not available Coordinatore Université Paris XII Contributo UE Nessun dato Indirizzo Route forestière Hurtault 77300 Fontainebleau Francia Mostra sulla mappa Costo totale Nessun dato Partecipanti (8) Classifica in ordine alfabetico Classifica per Contributo UE Espandi tutto Riduci tutto Armenian National Academy of Sciences Armenia Contributo UE Nessun dato Indirizzo P. Sevak street, 1 37044 Erevan Mostra sulla mappa Costo totale Nessun dato Russian Academy of Sciences Russia Contributo UE Nessun dato Indirizzo Fontanka, 27 191011 St. Petersburg Mostra sulla mappa Costo totale Nessun dato Taras Shevchenko National University of Kiev Ucraina Contributo UE Nessun dato Indirizzo 6, Glushkov av. 03127 Kiev Mostra sulla mappa Costo totale Nessun dato Udmurt State University Russia Contributo UE Nessun dato Indirizzo No 1, Universitetskaya 426034 Izhevsk Mostra sulla mappa Costo totale Nessun dato University of Athens Grecia Contributo UE Nessun dato Indirizzo 37, John Kennedy Street 16121 Kaisariani Mostra sulla mappa Costo totale Nessun dato University of Napoli 2 Italia Contributo UE Nessun dato Indirizzo via Vivaldi 43 81100 Caserta Mostra sulla mappa Costo totale Nessun dato Université Clermont 1 Francia Contributo UE Nessun dato Indirizzo Campus des Cézeaux 63172 Aubière Cedex Mostra sulla mappa Costo totale Nessun dato Université de Mons-Hainaut Belgio Contributo UE Nessun dato Indirizzo Avenue du Champ de Mars, 6 7000 Mons Mostra sulla mappa Costo totale Nessun dato