# One postdoctoral position in the scientific project "Between proof theory, reverse mathematics, and the model theory of arithmetic"

The project concerns various issues related to the model theory and proof theory of first- and second-order arithmetic. The three main research topics are:

- Models of collection principles, in particular expansions of models that satisfy collection but not induction for a given class of formulas.
- The first-order consequences of second-order statements (in particular combinatorial statements) over various base theories in second-order arithmetic.
- The development of a theory of proof sizes and proof speedup for subtheories of arithmetic.

The candidate should have research experience (documented by publications or preprints) in at least one of the following areas of mathematical logic: nonstandard models of arithmetic, proof theory of arithmetic, reverse mathematics.

The project „Between proof theory, reverse mathematics, and the model theory of arithmetic”, led by dr hab. Leszek Kołodziejczyk, is offering one postdoctoral position in the Institute of Mathematics at the Faculty of Mathematics, Informatics and Mechanics of the University of Warsaw.

## Terms of employment

The selected candidate will be employed as a full-time researcher (pol. adiunkt). The duration of employment is for one year, with possible extension for a second year. The starting date can be set between March 1, 2025 and October 1, 2025, as agreed upon by the candidate and the principal investigator. The offered basic salary is approx. 9 000 PLN gross/month. The position comes with no

teaching obligations. The selected candidate will work on problems related to one or more of the research directions studied within the project, which are described below.

## Description of the project

The project concerns various issues related to the model theory and proof theory of first- and second-order arithmetic. The three main research topics are:

- Models of collection principles, in particular expansions of models that satisfy collection but not induction for a given class of formulas.
- The first-order consequences of second-order statements (in particular combinatorial statements) over various base theories in second-order arithmetic.
- The development of a theory of proof sizes and proof speedup for subtheories of arithmetic

## Requirements

The candidate should have research experience (documented by publications or preprints) in at least one of the following areas of mathematical logic related to the topics of the project:

- nonstandard models of arithmetic,
- proof theory of arithmetic,
- reverse mathematics.

Experience in using nonstandard models to obtain provability or unprovability results will be an advantage. At the moment of employment, the successful candidate will be expected to hold a PhD degree in a discipline related to mathematical logic. The degree must be obtained no earlier than 7 years before the year of employment in the project. A PhD degree is not required at the time of application. The competition may be entered by candidates who meet the conditions set out in art. 113 of the Law

on Higher Education and Science of July 20, 2018 (Journal of Laws of 2023, item 742, as amended).

## Applications

An application should include:

- a signed cover letter addressed to the Dean of the Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, together with the personal data clause (attached);
- a copy of the PhD diploma; if the candidate does not yet have a PhD, a copy of the thesis or a description of the expected contents of the thesis, together with a statement concerning the expected date of obtaining the degree;
- a scientific CV with a list of publications;
- at most three recent publications.

In addition, two recommendation letters by senior researchers are required. They should be sent directly to the email address provided below. Applications, as well as further questions on both the scientific topic of the project and the formal details of the call procedure, should be directed to dr hab. Leszek Kołodziejczyk: lak@mimuw.edu.pl

In order to apply for the position, candidates should send an e-mail and submit the required documents as attached .pdf files.

**Application deadline: November 16, 2024**