Patrick Cegielski – författare

The field of weak arithmetics is an application of logical methods to number theory that was 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 first-order formulas with a finite number of alternations of quantifiers; a survey on a class of tools called pebble games; the fact that the reals e and pi have approximations expressed by first-order formulas using bounded quantifiers; properties of 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.

The field of weak arithmetics is an application of logical methods to number theory that was developed by mathematicians, philosophers, and theoretical computer scientists. New Studies in Weak Arithmetics is dedicated to late Australian mathematician Alan Robert Woods (1953-2011), whose seminal thesis is published here for the first time. This volume also contains the unpublished but significant thesis of Hamid Lesan (1951-2006) as well as other original papers on topics addressed in Woods' thesis and life's work that were first presented at the 31st Journees sur les Arithmetiques Faibles meeting held in Samos, Greece, in 2012.

This Festschrift is published in honor of Yuri Gurevich’s 80th birthday. An associated conference, YuriFest 2020, was planned for May 18–20 in Fontainebleau, France, in combination with the 39th Journées sur les Arithmétiques Faibles also celebrating Yuri’s 80th birthday. Because of the coronavirus situation, the conference had to be postponed, but this Festschrift is being published as originally planned. It addresses a very wide variety of topics, but by no means all of the fields of logic and computation in which Yuri has made important progress.