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
Participants
- Dino Rossegger (Technische Universität Wien)
- Mateusz Łełyk (University of Warsaw)
Publications
- Dichotomy results for classes of countable graphs
[ DOI
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arXiv
]
with Vittorio Cipriani, Ekaterina Fokina, Matthew Harrison-Trainor, and Liling Ko
submitted for publication (2025) - Uniformity in learning structures
[ DOI
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arXiv
]
with Vittorio Cipriani
submitted for publication (2025) - Classifying the complexity of models of arithmetic
[ DOI
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arXiv
]
with David Gonzalez, Mateusz Łełyk, and Patryk Szlufik
submitted for publication (2025)