#
JAF37

Trente-septièmes Journées sur les Arithmétiques Faibles

Thirty seventh Weak Arithmetics Days

Villa Finaly - Florence (Italy)

## Monday, May 28 2018

## Morning

- 9h:
*Registration*
- 9h45:
*Opening session*
- 10h: Olivier Finkel (Paris VII)
*Polishness of some topologies related to automata*
[Joint work with Olivier Carton and Dominique Lecomte]
- 10h30:
*Coffee break*
- 11h15: Laurence Kirby (Baruch College, CUNY)
*Bounded finite set theory*
- 11h45: Jana Glivická (Prague)
*Models of arithmetics with linear induction*

## Lunch (13h)

## Afternoon

- 14h30: Eugenio Omodeo (Trieste, Italy)
*Further reflections on candidate “rule-them-all" Diophantine equations*
[Joint work with Domenico Cantone]
- 15h00: Mihail Starchak (Saint Petersburg)
*Two Classes of Basic Divisibility Families from NP*
- 15h30:
*Coffee break*
- 16h15: Petr Glivický (Prague)
*Fermat’s last theorem and Catalan’s conjecture in arithmetics with weak exponentiation*

## Tuesday, May 29 2018

## Morning

- 9h30: Julien Cervelle (Paris 12)
*Study of stepwise simulation between ASMs*
[Joint work with Patrick Cégielski]
- 10h: Charalampos Cornaros (University of Aegean, Greece)
*Products of primes in weak systems of arithmetic*
- 10h30:
*Coffee break*
- 11h15: Yuri Gurevich (Ann Arbor)
*LOGIC in computer science, computer engineering and mathematics*

## Lunch (13h)

## Afternoon

- 14h30: Fedor Pakhomov (Steklov Institute, Moscow)
*Weak Set Theories and* Δ_{0}-*Collection*
- 15h30: Costas Dimitracopoulos (Athens)
*End extensions of models of fragments of PA*
[Joint work with Vasileios Paschalis]
- 16h00:
*Coffee break*
- 16h45: Jean-Eric Pin (Paris VII)
*Regular languages, profinite topologies and weak arithmetic*

## 19h00: Special Dinner

## Wednesday, May 30 2018

- 10h: Pierre Valarcher (Paris 12)
*Primitive recursion and algorithmically-completeness for Primitive Recursive Class of functions*
[Joint work with Patrick Cégielski, Julien Cervelle, and Serge Grigorieff]
- 10h30:
*Coffee break*
- 11h15: Mateusz Lelyk (Poland)
*How useful are pure compositional axioms for the truth predicate*?

## 12h15: Closure

## Lunch (12h30)