Logic List Mailing Archive

CfA: Postdoc in Logic (“Structural Complexity Measures for Foundational Theories”), University of Warsaw (Poland), Deadline 3 December 2025

Dear All,

University of Warsaw, Faculty of Philosophy is offering a post-doc position for 24 months to work within the project "Structural complexity measures for foundational theories". The deadline for the submissions is the 3rd of December.

The main goal of the project, co-run with the Technical University of Vienna (TUV)  is to analyze the Scott ranks of models of foundational theories, such as

 ● Peano Arithmetic (PA) and its subsystems based on restricted collection and induction schemes. 

● Second-Order Arithmetic (𝑍2) and its subsystems based on restricted comprehension scheme. 

● Zermelo-Fraenkel Set Theory (ZF) and its subsystems. 

The Scott rank of the given countable model is the ordinal number that is the complexity of the simplest sentence in the infinitary logic (allowing countable Boolean operations) which uniquely (up to an isomorphism) describes the given model among other countable models. As famously proved by Scott, each countable structure does have a rank. A Scott function for a theory T is a function which given a countable ordinal number 𝛼 as input, returns the number of countable models of T of rank 𝛼.The far-reaching goal of the project is to determine the Scott functions for the above described theories and their completions. Additionally, we aim at determining the general properties of Scott functions. This kind of investigation requires a creative mixture of tools from computability theory, descriptive set-theory, nonstandard models of arithmetic and set theory.  The project was initiated by Montalbán and Rossegger paper “The Structural Complexity of Models of Arithmetic” (https://doi.org/10.1017/jsl.2023.43). The preliminary research outcomes are presented in  the paper by Gonzalez, Łełyk, Rossegger and Szlufik “Classifying the Complexity of Models of Arithmetic” (https://arxiv.org/abs/2507.12025). 

Full information about the appointment conditions and the recruitment procedure can be found at Euraxess

https://euraxess.ec.europa.eu/jobs/385435

Best,
Mateusz Łełyk
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