FWF International Project I6087

The project has a Polish parter project lead by Grigor Sargsyan, IMPAN.

Classifying Derived Models of the Axiom of Determinacy

This project started on February 1, 2023 and will run until January 31, 2026. The awarded grants are 366,628.50€.

Publications submitted or published within this project

1. Towards a generic absoluteness theorem for Chang models
   (with G. Sargsyan)

   Advances in Mathematics. Volume 476, August 2025.
   DOI: 10.1016/j.aim.2025.110357. PDF. arXiv. Bibtex.

    @ARTICLE{MS_GenAbsCM,
      AUTHOR= {S. Müller and G. Sargsyan},
      TITLE= {Towards a generic absoluteness theorem for Chang models},
      JOURNAL={Advances in Mathematics},
      VOLUME = {476},
      ISSUE = {},
      YEAR = {2025},
      PAGES = {},
      EPRINT = {2304.07623},
      DOI = {10.1016/j.aim.2025.110357}}

2. A model with fragments of projective determinacy and failures of DC
   (with B. Wcisło)

   Submitted. PDF. arXiv. Bibtex.

    @ARTICLE{MuWc_PDnoDC,
      AUTHOR = {S. Müller and B. Wcisło},
      TITLE = {A model with fragments of projective determinacy and failures of DC},
      JOURNAL = {},
      VOLUME = {},
      ISSUE = {},
      YEAR = {2025},
      PAGES = {},
      EPRINT = {2505.16628},
      DOI = {}}

3. The lambda-PSP at lambda-coanalytic sets
   (with F. Barrera and V. Dimonte)

   Submitted. PDF. arXiv. Bibtex.

    @ARTICLE{BaDiMu25,
      AUTHOR = {F. Barrera and V. Dimonte and S. Müller},
      TITLE = {The $\lambda$-PSP at $\lambda$-coanalytic sets},
      JOURNAL = {},
      VOLUME = {},
      ISSUE = {},
      YEAR = {2025},
      PAGES = {},
      EPRINT = {2504.15675},
      DOI = {}}

4. Gödel's Program in Set Theory
   (with G. Sargsyan)

   Monatshefte für Mathematik. Special volume in honor of Gödel, April 2025.
   DOI: 10.1007/s00605-025-02086-x. PDF. arXiv. Bibtex.

    @ARTICLE{MuSa25,
      AUTHOR = {S. Müller and G. Sargsyan},
      TITLE = {Gödel's Program in Set Theory},
      JOURNAL = {Monatshefte für Mathematik},
      VOLUME = {Special volume in honor of Gödel}
      ISSUE = {},
      YEAR = {2025},
      PAGES = {},
      EPRINT = {2412.07325},
      DOI = {10.1007/s00605-025-02086-x}}

5. Outward compactness
   (with P. Holy and P. Lücke)

   Israel Journal of Mathematics, accepted. PDF. arXiv. Bibtex.

    @ARTICLE{HLM24,
      AUTHOR = {P. Holy and P. Lücke and S. Müller},
      TITLE = {Outward compactness},
      JOURNAL = {Israel Journal of Mathematics},
      VOLUME = {},
      ISSUE = {},
      YEAR = {2024},
      PAGES = {},
      EPRINT = {2402.15788},
      DOI = {}}

6. Sigma_1-definability at higher cardinals: Thin sets, almost disjoint families and long well-orders
   (with P. Lücke)

   Forum of Mathematics, Sigma. Volume 11, 2023. e103.
   DOI: 10.1017/fms.2023.102. PDF. arXiv. Bibtex.

    @ARTICLE{LM23,
      AUTHOR = {P. Lücke and S. Müller},
      TITLE = {Sigma_1-definability at higher cardinals: Thin sets, almost disjoint families and long well-orders},
      JOURNAL = {Forum of Mathematics, Sigma},
      VOLUME = {11},
      ISSUE = {},
      YEAR = {2023},
      PAGES = {},
      EPRINT = {2110.01468},
      DOI = {10.1017/fms.2023.102}}

7. Chang models over derived models with supercompact measures
   (with T. Gappo and G. Sargsyan)

   Journal of Mathematical Logic, accepted. PDF. arXiv. Bibtex.

    @ARTICLE{GMS23,
      AUTHOR= {T. Gappo and S. Müller and G. Sargsyan},
      TITLE= {Chang models over derived models with supercompact measures},
      JOURNAL={Journal of Mathematical Logic},
      VOLUME = {},
      ISSUE = {},
      YEAR = {2023},
      PAGES = {},
      EPRINT = {2307.08607},
      DOI = {10.1142/S0219061325500072}}

8. Towards a generic absoluteness theorem for Chang models
   (with G. Sargsyan)

   Advances in Mathematics. Volume 476, August 2025. 110357.
   DOI: 10.1016/j.aim.2025.110357. PDF. arXiv. Bibtex.

    @ARTICLE{MS_GenAbsCM,
      AUTHOR= {S. Müller and G. Sargsyan},
      TITLE= {Towards a generic absoluteness theorem for Chang models},
      JOURNAL={Advances in Mathematics},
      VOLUME = {476},
      ISSUE = {},
      YEAR = {2025},
      PAGES = {110357},
      EPRINT = {2304.07623},
      DOI = {10.1016/j.aim.2025.110357}}

9. Determinacy and Large Cardinals
   

   Logic and Its Applications. Lecture Notes in Computer Science. Volume 13963.
   PDF. Bibtex.

    @INPROCEEDINGS{MuICLA,
      AUTHOR= {S. Müller},
      TITLE= {Determinacy and Large Cardinals},
      SERIES = {Lecture Notes in Computer Science},
      BOOKTITLE = {Logic and Its Applications},
      VOLUME = {13963},
      YEAR = {},
      PAGES = {},
      DOI = {}}