Aim. Weak arithmetics play a fundamental role in several areas of philosophy, mathematics, and computer science, by studying the nature and properties of natural numbers from a logical point of view. The aim of the conference is to provide a forum for researchers to present their results to members of communities who study or apply weak arithmetics in various fields and formalisms. Previous JAFs.
Topics. Proofs in arithmetic with restricted system of axioms; non-standard models of such systems; decidability, undecidability, and complexity of arithmetical theories; definability in arithmetic structures; machines, automata and words, related to arithmetic; finite model theory, word structures.
Location. Institute of Mathematics, Czech Academy of Sciences. The institute is in the centre of Prague, a few minutes walk from Wenceslas Square. The address is Žitná 25, 110 00 Praha 1.
Invited speakers. Albert Atserias, Technical University of Catalonia; Emil Jeřábek, Czech Academy of Sciences; Leszek Kołodziejczyk, University of Warsaw; Jan Krajíček, Charles University
Programme.
Monday September 8
09:30 Emil Jeřábek, Mathematics in VTC0
10:30 coffee break
11:00 Alexei Semenov, Definability lattices for very weak arithmetics
11:30 Juvenal Murwanashyaka, Variants of adjunctive set theory which are not sequential
12:00 end of morning session
14:00 Jan Krajíček, Extensions of models of bounded arithmetic
15:00 coffee break
15:30 Ondřej Ježil, Prime factorization in models of PV1
16:00 Julien Daoud, Speedups for Presburger Arithmetic and real closed fields
16:30 end of talks
17:00 business meeting
09:30 Albert Atserias, Axiomatic strength of hitting sets for multivariate polynomials within bounded arithmetic
10:30 coffee break
11:00 Azza Gaysin, Proof complexity of Mal’tsev CSPs
11:30 Piotr Gruza, Tightness and semantic tightness in subtheories of Peano arithmetic
12:00 end of morning session
14:00 excursion
19:00 conference dinner
09:30 Leszek Kołodziejczyk, Gauging the strength of (infinite) Ramsey's theorem for pairs: first-order consequences,
the effect of the base theory, influence on proof size
10:30 coffee break
11:00 Quentin Le Houerou, Ramsey-like theorems for separable permutations
11:30 Mengzhou Sun, On the finite cohesiveness principle
12:00 end of morning session
14:00 Patryk Szlufik, Scott ranks of models of elementary arithmetic
14:30 Mykyta Narusevych, Why is it hard to separate T^2_2(R) from T^\infty_2(R) via forcing?
15:00 coffee break
15:30 Erfan Khaniki, From proof complexity to circuit complexity via interactive protocols
16:00 end
Contributed talks. Authors are invited to send an abstract not exceeding three pages as an electronic submission in the form of a pdf file, to be sent both to cegielski@u-pec.fr and to thapen@math.cas.cz. Submissions are to be received before 7 July 2025.
Accommodation. There are many hotels within walking distance. Two very close nearby, which the institute sometimes uses for visitors, are EA Hotel New Town and Hotel Archibald City. We have not made any special arrangements with them for the meeting.
Registration. To register, send your details (full name, affiliation, planned dates of arrival and departure) to thapen@math.cas.cz. There is no conference fee. Please register if possible by 17 August so we have an idea of numbers.
Contact. For any enquires contact Patrick Cégielski, cegielski@u-pec.fr or Neil Thapen, thapen@math.cas.cz.
JAF steering committee. Patrick Cégielski (Paris XII), Julien Cervelle (Paris XII), Andrés Córdon-Franco (Seville), Ali Enayat (Göteborg), Costas Dimitracopoulos (Athens), Alex Esbelin (Clermont-Ferrand), Neil Thapen (CAS)
Local organizing committee. Neil Thapen (CAS), Pavel Hrubeš (CAS), Ondřej Ježil (Charles University)
Sponsors / organizers.
Header image of the astronomical clock in Old Town Square by Txllxt TxllxT, CC BY-SA 4.0