New Studies in Weak Arithmetics
Edited by Patrick Cégielski, Charalampos Cornaros, and Costas
Dimitracopoulos
The field of weak arithmetics is application of logical methods to Number
Theory, developed by mathematicians, philosophers, and theoretical
computer scientists. In this volume, after a general presentation of weak
arithmetics, the following topics are studied: the properties of integers
of a real closed field equipped with exponentiation; conservation results
for the induction schema restricted to firstorder formulas with a finite
number of alternations of quantifiers; a survey on a class of tools,
called pebble games, used in finite model theory; the fact that reals e
and π have approximations expressed by firstorder formulas using
bounded quantifiers; properties on infinite pictures depending on the
universe of sets used; a language that simulates in a sufficiently nice
manner all algorithms of a certain restricted class; the logical
complexity of the axiom of infinity in some variants of set theory without
the axiom of foundation; and the complexity to determine whether a trace
is included in another one.
Patrick Cégielski, Professor at University
ParisEst Créteil – IUT de Sénart Fontainebleau, is
the coordinator of a European consortium of teams working on weak
arithmetics, mainly from Armenia, Belgium, Czech Republic, Federation of
Russia, France, United Kingdom, Greece, Israel, Italy, Poland, Portugal,
Slovakia, Spain, Tunisia, and Ukraine.
Jointly published with Presses Universitaires
du Pôle de Recherche
et d'enseignement supérieur ParisEst. See
also Studies in Weak Arithmetics.
 Foreword by Luc Hittinger
 Greetings by Petros Parianos
 Introduction by Patrick Cégielski, Charalampos Cornaros, and Constantin Dimitracopoulos
 I. Contributions
 A few questions concerning consistency and conservativeness,
by Zofia Adamowicz
 In memoriam of Alan Robert Woods
by Patrick Cégielski and Denis Richard
 Degres Ludiques : une introduction
by C. Chalons and JeanPierre Ressayre
 Primes in Models of I0 + 1: Density in Henselizations
by Paola D'Aquino and Angus Macintyre
 A New Proof of Tanaka's Theorem
by Ali Enayat
 0definability of the denumerant with one plus three variables
by HenriAlex Esbelin
 Techniques in weak analysis for conservation results
by Antonio M. Fernandes, Fernando Ferreira,
and Gilda Ferreira
 Adding standardness to nonstandard arithmetic
by Richard Kaye, Roman Kossak, and Tin Lok Wong
 On the Notion of Proving its own Consistency
by Doukas Kapantais
 Randomness, pseudorandomness and models of arithmetic
by Pavel Pudlak
 The asymptotic behaviour of the number of trees in certain classes
by JanChristoph SchlagePuchta
 What is Sequentiality?
by Albert Visser
 II. Some problems in Logic and Number Theory, and their connections
Thesis (1981) of Alan Robert Woods
Note by Costas Dimitracopoulos
 III. Models of Arithmetic
Thesis (1978) of H. Lessan
Note by George Wilmers
September 2013
ISBN (Paperback): 9781575867236
ISBN (electronic): 9781575867243

Distributed by the University of Chicago Press
