This project studies the structural complexity of foundational theories and investigates when a theory has an intended model. We use advances in Scott analysis and new techniques to understand how intendedness arises, and how model‑theoretic complexity can be detected by infinitary logic.

Research questions

  • Do foundational theories have a structurally simplest model, and is it the intended one?
  • Can intendedness be characterized by other properties of the theory?
  • How do Scott functions reflect model‑theoretic and descriptive‑set‑theoretic complexity?

Approach

We combine tools from Scott analysis with methods from the foundations of mathematics. The project is interdisciplinary and international, with regular collaboration between the teams in Vienna and Warsaw.

Funding

This project is funded by the Austrian Science Fund (FWF) and by the Polish Science Foundation (NCN). See the FWF project page

Team

  • Dino Rossegger (Technische Universität Wien, PI Austrian side)
  • Mateusz Łełyk (University of Warsaw, PI Polish side)

Publications

  1. A topological highness notion pdf
    Dino Rossegger
    Proceedings of the Panhellenic Logic Symposium, vol. 15, pp. 1-7 (2026)
  2. Scott Analysis below the Vaught Ordinal DOI arXiv
    David Gonzalez, Dino Rossegger, and Dan Turetsky
    submitted for publication (2026)
  3. Structural vs. computational complexity DOI arXiv
    Johanna N. Y. Franklin, Dino Rossegger, and Dan Turetsky
    submitted for publication (2026)
  4. Dichotomy results for classes of countable graphs DOI arXiv
    Vittorio Cipriani, Ekaterina Fokina, Matthew Harrison-Trainor, Liling Ko, and Dino Rossegger
    submitted for publication (2025)
  5. Uniformity in learning structures DOI arXiv
    Vittorio Cipriani and Dino Rossegger
    submitted for publication (2025)
  6. Classifying the complexity of models of arithmetic DOI arXiv
    David Gonzalez, Mateusz Łełyk, Dino Rossegger, and Patryk Szlufik
    submitted for publication (2025)