This is the project page of the project ACOSE - Algorithmic complexity of structural equivalence relations funded by a Marie Skłodowska Curie Global Fellowship under Horizon 2020 of the European Commission.

The goal of this project is to investigate the relationship between notions of complexity in computable structure theory and notions of complexity in descriptive set theory. The project consist of a two year outgoing phase at the University of California, Berkeley and a one year return phase at Technische Universität Wien.

Participants

  • Principal Investigator: Dino Rossegger
  • Supervision Outgoing phase: Antonio Montalbán
  • Supervision Return phase: Ekaterina Fokina

Talks

  1. Recursive isomorphism and Turing equivalence through the effective descriptive set theory lens (Black board talk)
    Generalized Computability theory 2024, Castro Urdiales, Spain, 22.08.24
  2. Algorithmic Aspects of Left-orderings of solvable Baumslag-Solitar groups via their dynamical realizations, [ Slides ]
    Computability in Europe, 11.07.2024
  3. Learning equivalence relations on Polish spaces (Black board talk)
    Leeds Computability Days, University of Leeds, 02.07.2024
  4. The Borel complexity of first-order theories [ Slides ]
    Logic Seminar, Ghent University, 06.03.2024
  5. The Borel complexity of first-order theories [ Slides | Video ]
    Models of Peano Arithmetic seminar, City University of New York, 13.02.2024
  6. The Borel complexity of first-order theories [ Slides | Video ]
    World Logic Day workshop, Nazarbayev University, 14.01.2024
  7. Structural complexity notions for foundational theories [ Slides ]
    Logic Seminar, Kurt Gödel Research Center, 09.11.2023
  8. Structural complexity notions for foundational theories [ Slides ]
    Pennstate Logic Seminar, 07.11.2023
  9. Learning equivalence relations [ Slides ]
    Online Logic Seminar, 19.10.2023
  10. The strong degrees of categoricity above 0" [ Slides ]
    Logic Seminar, University of Wisconsin at Madison, 18.04.2023
  11. The strong degrees of categoricity above 0" [ Slides ]
    Logic Seminar, University of Michigan at Ann Arbor, 12.04.2023
  12. Pairs of Structures: Variations and Application [ Slides ]
    Plenary Talk, ASL Annual Meeting 2023, UC Irvine, 28.03.2023
  13. The strong degrees of categoricity above 0" [ Slides ]
    Logic Seminar, Iowa State University, 01.03.2023
  14. The Structural Complexity of Models of Arithmetic [ Slides ]
    California State University, Northridge, 30.11.2022
  15. Analytic complete equivalence relations and their degree spectra [ Slides ]
    Caltech Logic Seminar, 02.11.2022
  16. The degrees of categoricity above 0 double jump [ Slides ]
    Logic Colloquium, University of California, Berkeley, 07.10.2022
  17. The Structural Complexity of Models of Arithmetic [ Slides ]
    ASL Logic Colloquium 2022, Reykjavik, Iceland, 01.07.2022
  18. The Structural Complexity of Models of Arithmetic [ Slides | Video ]
    Models of Peano Arithmetic seminar, City University of New York, 03.05.2022
  19. The Structural Complexity of Models of Arithmetic [ Slides ]
    Computability Special Session, ASL Annual Meeting at Cornell University 2022, 09.04.2022
  20. New Examples of Degrees of Categoricity [ Slides | Video ]
    Computability Theory and Applications, 02.11.2021

Publications

  1. Scott sentence complexities of linear orderings [ DOI ]
    with David Gonzalez
    The Journal of Symbolic Logic (2024)
  2. Hausdorff dimension and countable Borel equivalence relations [ DOI ]
    with Andrew Marks, and Theodore Slaman
    submitted for publication (2024)
  3. Feferman's completeness theorem [ DOI ]
    with Fedor Pakhomov, and Michael Rathjen
    submitted for publication (2024)
  4. Learning Equivalence Relations on Polish Spaces [ DOI | arXiv ]
    with Theodore Slaman, and Tomasz Steifer
    submitted for publication (2024)
  5. A Lopez-Escobar Theorem for Continuous Domains [ DOI | arXiv ]
    with Nikolay Bazhenov, Ekaterina Fokina, Alexandra Soskova, and Stefan Vatev
    The Journal of Symbolic Logic vol. First View (2024)
  6. The Borel complexity of the class of models of first-order theories [ DOI | arXiv ]
    with Uri Andrews, David Gonzalez, Steffen Lempp, and Hongyu Zhu
    submitted for publication (2024)
  7. Algorithmic Aspects of Left-Orderings of Solvable Baumslag–Solitar Groups via its Dynamical Realization [ DOI | arXiv ]
    with Meng-Che “Turbo” Ho, and Khanh Le
    Twenty Years of Theoretical and Practical Synergies, Computability in Europe, Lecture Notes in Computer Science vol. 14773, 72-84 (2024)
  8. Learning Families of Algebraic Structures from Text [ DOI | arXiv ]
    with Nikolay Bazhenov, Ekaterina Fokina, Alexandra Soskova, and Stefan Vatev
    Twenty Years of Theoretical and Practical Synergies, Computability in Europe, Lecture Notes in Computer Science vol. 14773, 166-178 (2024)
  9. Degrees of categoricity and treeable degrees [ DOI | arXiv ]
    with Barbara F. Csima
    Journal of Mathematical Logic (2023)
  10. The structural complexity of models of arithmetic [ DOI | arXiv ]
    with Antonio Montalbán
    The Journal of Symbolic Logic vol. First View (2023)
  11. Degree spectra of analytic complete equivalence relations [ DOI | arXiv ]
    The Journal of Symbolic Logic vol. 87 (4) , 1663-1676 (2022)
  12. Relations enumerable from positive information [ DOI | arXiv ]
    with Barbara F. Csima, and Luke MacLean
    submitted for publication (2022)