Publications

1. 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 = {}}

2. 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 = {}}

3. 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 = {}}

4. 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}}

5. The consistency strength of determinacy when all sets are universally Baire
   

   Advances in Mathematics. Volume 481, December 2025
   DOI: 10.1016/j.aim.2025.110548. PDF. arXiv. Bibtex.

    @ARTICLE{Mu21,
      AUTHOR= {S. Müller},
      TITLE= {The consistency strength of determinacy when all sets are universally {B}aire},
      JOURNAL = {Advances in Mathematics},
      VOLUME = {481}
      ISSUE = {},
      YEAR = {2025},
      PAGES = {},
      EPRINT ={2106.04244},
      DOI = {10.1016/j.aim.2025.110548}}

6. 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}}

7. 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}}

8. 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}}

9. An undecidable extension of Morley's theorem on the number of countable models
   (with C. J. Eagle, C. Hamel, and F. D. Tall)

   Annals of Pure and Applied Logic. Volume 174, Issue 9, October-November 2023. 103317.
   DOI: 10.1016/j.apal.2023.103317. PDF. arXiv. Bibtex.

    @ARTICLE{EHMT23,
      AUTHOR= {C. J. Eagle and C. Hamel and S. Müller and F. D. Tall},
      TITLE= {An undecidable extension of {Morley's theorem} on the number of countable
    models},
      JOURNAL={Annals of Pure and Applied Logic},
      EPRINT ={2107.07636},
      VOLUME = {174},
      ISSUE = {9},
      YEAR = {2023},
      PAGES = {103317},
      DOI = {10.1016/j.apal.2023.103317}}
      

10. 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}}

11. Uniformization and Internal Absoluteness
    (with P. Schlicht)

    Proc. Amer. Math. Soc. Volume 151, 2023. Pages 3089-3102.
    DOI: 10.1090/proc/16155. PDF. arXiv. Bibtex.

     @ARTICLE{MSch23,
       AUTHOR= {S. Müller and P. Schlicht},
       TITLE= {Uniformization and Internal Absoluteness},
       JOURNAL={Proc. Amer. Math. Soc.},
       EPRINT ={2108.09688},
       VOLUME = {151},
       YEAR = {2023},
       PAGES = {3089--3102},
       DOI = {10.1090/proc/1615}}

12. Perfect Subtree Property for Weakly Compact Cardinals
    (with Y. Hayut)

    Israel Journal of Mathematics. Volume 253, March 2023. Pages 865-886.
    DOI: 10.1007/s11856-022-2385-4. PDF. arXiv. Bibtex.

     @ARTICLE{HM19,
       AUTHOR= {Y. Hayut and S. Müller},
       TITLE= {Perfect subtree property for weakly compact cardinals},
       JOURNAL={Israel Journal of Mathematics},
       VOLUME = {253},
       ISSUE = {},
       YEAR = {2023},
       PAGES = {865--886},
       EPRINT = {1910.05159},
       DOI = {10.1007/s11856-022-2385-4}}

13. Constructing Wadge classes
    (with R. Carroy and A. Medini)

    Bulletin of Symbolic Logic. Volume 28, Issue 2, June 2022. Pages 207-257.
    DOI: 10.1017/bsl.2022.7. PDF. arXiv. Bibtex.

     @ARTICLE{CMM22,
       AUTHOR= {R. Carroy and A. Medini and S. Müller},
       TITLE= {Constructing {W}adge classes},
       JOURNAL={The Bulletin of Symbolic Logic},
       VOLUME = {28},
       ISSUE = {2},
       YEAR = {2022},
       PAGES = {207--257},
       EPRINT ={1907.07612}}

14. Lebesgue's density theorem and definable selectors for ideals
    (with P. Schlicht, D. Schrittesser, and T. Weinert)

    Israel Journal of Mathematics. Volume 249, May 2022. Pages 501-551.
    DOI: 10.1007/s11856-022-2312-8. PDF. arXiv. Bibtex.

     @ARTICLE{MSSW22,
       AUTHOR = {S. Müller and P. Schlicht and D. Schrittesser and T. Weinert},
       TITLE = {Lebesgue's density theorem and definable selectors for ideals},
       JOURNAL={Israel Journal of Mathematics},
       VOLUME = {249},
       YEAR = {2022},
       PAGES = {501--551},
       EPRINT = {1811.06489},
       DOI = {10.1007/s11856-022-2312-8} }

15. HOD in inner models with Woodin cardinals
    (with G. Sargsyan)

    The Journal of Symbolic Logic. Volume 86, Issue 3, September 2021. Pages 871-896.
    DOI: 10.1017/jsl.2021.61. PDF. arXiv. Bibtex.

     @ARTICLE{MS21,
       AUTHOR= {S. Müller and G. Sargsyan},
       TITLE= {H{OD} in inner models with {W}oodin cardinals},
       JOURNAL={Journal of Symbolic Logic},
       VOLUME = {86},
       ISSUE = {3},
       YEAR = {2021},
       PAGES = {871-896}, 
       DOI = {10.1017/jsl.2021.61},
       EPRINT = {2004.09201}}

16. The consistency strength of determinacy when all sets are universally Baire
    

    Advances in Mathematics. Volume 481, December 2025
    DOI: 10.1016/j.aim.2025.110548. PDF. arXiv. Bibtex.

     @ARTICLE{Mu21,
       AUTHOR= {S. Müller},
       TITLE= {The consistency strength of determinacy when all sets are universally {B}aire},
       JOURNAL = {Advances in Mathematics},
       VOLUME = {481}
       ISSUE = {},
       YEAR = {2025},
       PAGES = {},
       EPRINT ={2106.04244},
       DOI = {10.1016/j.aim.2025.110548}}

17. Closure properties of measurable ultrapowers
    (with P. Lücke)

    The Journal of Symbolic Logic. Volume 86, Issue 2, June 2021. Pages 762-784.
    DOI: 10.1017/jsl.2021.29. PDF. arXiv. Bibtex.

     @ARTICLE{LM21,
       AUTHOR= {P. Lücke and S. Müller},
       TITLE= {Closure properties of measurable ultrapowers},
       JOURNAL={Journal of Symbolic Logic},
       VOLUME = {86},
       ISSUE = {2},
       YEAR = {2021},
       PAGES = {762--784}, 
       DOI = {10.1017/jsl.2021.29},
       EPRINT ={2009.09530}}

18. Structural Properties of the Stable Core
    (with S.-D. Friedman and V. Gitman)

    The Journal of Symbolic Logic. Volume 88, Issue 3, September 2023. Pages 889-918.
    DOI: 10.1017/jsl.2023.10. PDF. arXiv. Bibtex.

     @ARTICLE{FGM19,
       AUTHOR= {S.-D. Friedman and V. Gitman and S. Müller},
       TITLE= {Structural properties of the stable core},
       JOURNAL={Journal of Symbolic Logic},
       VOLUME = {88},
       ISSUE = {3},
       YEAR = {2023},
       PAGES = {889--918},
       EPRINT ={1910.02265},
       DOI = {10.1017/jsl.2023.10}}

19. Infinite decreasing chains in the Mitchell order
    (with O. Ben-Neria)

    Archive for Mathematical Logic. Volume 60, March 2021. Pages 771-781.
    DOI: 10.1007/s00153-021-00762-x. PDF. arXiv. Bibtex.

     @ARTICLE{BNM21,
       AUTHOR= {O. Ben-Neria and S. Müller},
       TITLE= {Infinite decreasing chains in the {M}itchell order},
       JOURNAL={Archive for Mathematical Logic},
       VOLUME = {60},
       YEAR = {2021},
       PAGES = {771--781},
       DOI ={10.1007/s00153-021-00762-x},
       EPRINT ={1908.10224}}

20. Projective Games on the Reals
    (with J. Aguilera)

    Notre Dame Journal of Formal Logic. Volume 61, Issue 4, November 2020. Pages 573-589.
    DOI: 10.1215/00294527-2020-0027. PDF. arXiv. Bibtex.

     @ARTICLE{AM20b,
       AUTHOR= {J. Aguilera and S. Müller},
       TITLE = {Projective games on the reals},
       JOURNAL = {Notre Dame Journal of Formal Logic},
       VOLUME = {61},
       ISSUE = {4},
       YEAR = {2020},
       PAGES = {573-589},
       DOI = {10.1215/00294527-2020-0027},
       EPRINT = {1907.03583}}

21. The consistency strength of long projective determinacy
    (with J. Aguilera)

    The Journal of Symbolic Logic. Volume 85, Issue 1, March 2020. Pages 338-366.
    DOI: 10.1017/jsl.2019.78. PDF. arXiv. Bibtex.

     @ARTICLE{AM20a,
       AUTHOR= {J. Aguilera and S. Müller},
       TITLE= {The consistency strength of long projective determinacy},
       JOURNAL={Journal of Symbolic Logic},
       VOLUME = {85},
       ISSUE = {1},
       YEAR = {2020},
       PAGES = {338-366},
       DOI = {10.1017/jsl.2019.78},
       EPRINT ={1906.11949}}

22. The Axiom of Determinacy implies Dependent Choice in mice
    

    Mathematical Logic Quarterly. Volume 65, Issue 3, October 2019. Pages 370-375.
    DOI: 10.1002/malq.201800077. PDF. arXiv. Bibtex.

     @ARTICLE{Mu19,
    	AUTHOR = {S. Müller},
    	TITLE = {The axiom of determinacy implies dependent choice in mice},
    	JOURNAL = {Mathematical Logic Quarterly},
    	VOLUME = {65},
    	NUMBER = {3},
    	PAGES = {370-375},
    	YEAR = {2019},
    	DOI = {10.1002/malq.201800077},
    	URL = {https://onlinelibrary.wiley.com/doi/abs/10.1002/malq.201800077},
    	EPRINT = {1907.02755}}
    

23. Long games and sigma-projective sets
    (with J. Aguilera and P. Schlicht)

    Annals of Pure and Applied Logic. Volume 172, Issue 4, April 2021. 102939.
    DOI: 10.1016/j.apal.2020.102939. PDF. arXiv. Bibtex.

     @ARTICLE{AMS21,
       AUTHOR= {J. Aguilera and S. Müller and P. Schlicht},
       TITLE= {Long games and {$\sigma$-projective} sets},
       JOURNAL = {Annals of Pure and Applied Logic},
       VOLUME = {172},
       ISSUE = {4},
       YEAR = {2021},
       PAGES = {102939},
       DOI = {10.1016/j.apal.2020.102939},
       EPRINT = {2011.04947}}

24. Every zero-dimensional homogeneous space is strongly homogeneous under determinacy
    (with R. Carroy and A. Medini)

    Journal of Mathematical Logic. Volume 20, Issue 3, March 2020. 2050015.
    DOI: 10.1142/S0219061320500154. PDF. arXiv. Bibtex.

     @ARTICLE{CMM20,
       AUTHOR= {R. Carroy and A. Medini and S. Müller},
       TITLE= {Every zero-dimensional homogeneous space is strongly homogeneous under determinacy},
       JOURNAL= {Journal of Mathematical Logic},
       VOLUME = {20},
       ISSUE = {3},
       YEAR = {2020},
       PAGES = {2050015},
       DOI = {10.1142/S0219061320500154},
       EPRINT ={1806.00332} }

25. Mice with Finitely many Woodin Cardinals from Optimal Determinacy Hypotheses
    (with R. Schindler and W. H. Woodin)

    Journal of Mathematical Logic. Volume 20, Issue Supp01, October 2020. 1950013.
    DOI: 10.1142/S0219061319500132. PDF. arXiv. Bibtex.

     @ARTICLE{MSW20,
       AUTHOR= {S. Müller and R. Schindler and W.H. Woodin},
       TITLE= {Mice with finitely many {W}oodin cardinals from optimal determinacy hypotheses},
       JOURNAL={Journal of Mathematical Logic},
       VOLUME = {20},
       ISSUE = {Supp01},
       DOI = {10.1142/S0219061319500132},
       EPRINT ={1902.05890},
       YEAR = {2020}}

Reviews

26. 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 = {}}

27. Consistency strength lower bounds for the proper forcing axiom via the core model induction
    

    Bulletin of Symbolic Logic. Volume 26, Issue 1, December 2020. Pages 89-92.
    DOI: 10.1017/bsl.2020.6. PDF. Bibtex.

     @ARTICLE{MuReview,
       AUTHOR= {S. Müller},
       TITLE= {Consistency strength lower bounds for the proper forcing axiom via the core model induction},
       JOURNAL = {Bulletin of Symbolic Logic},
       NOTE = {Review of four papers by G.\ Sargsyan, J.\ Steel and N.\ Trang on consistency strength lower bounds for the proper forcing axiom via the core model induction.},
       VOLUME = {26},
       NUMBER = {1},
       YEAR = {2020},
       PAGES = {89-92},
       DOI = {10.1017/bsl.2020.6}}

Other Writings

• Pure and Hybrid Mice with Finitely Many Woodin Cardinals from Levels of Determinacy
  

  Dissertation. PDF. Bibtex.

   @phdthesis{Uh16,
     author = {S. Uhlenbrock},
     title = {Pure and {H}ybrid {M}ice with {F}initely {M}any {W}oodin {C}ardinals from {L}evels of {D}eterminacy},
     school = {WWU Münster},
     year = 2016 }
  

• Writeup of an account of Woodin’s HOD conjecture
  

  Masterthesis (in German). PDF

Interdisciplinary Publications

• Pulse Wave Analysis and Pulse Wave Velocity for Fistula Assessment
  (with N. Mueller, J. Streis, H. Pavenstädt, T. Felderhoff, S. Reuter and V. Busch)

  Kidney & Blood Pressure Research. Volume 45, Issue 4, July 2020. Pages 576-588.
  DOI: 10.1159/000506741. PDF. Bibtex.

   @ARTICLE{PWA,
  	AUTHOR = {N. Mueller and J. Streis and S. Müller and H. Pavenstädt and T. Felderhoff and S. Reuter and V. Busch},
  	TITLE = {Pulse wave analysis and pulse wave velocity for fistula assessment},
  	JOURNAL = {Kidney \& Blood Pressure Research},
  	VOLUME = {45},
  	NUMBER = {4},
  	PAGES = {576-588},
  	YEAR = {2020},
  	DOI = {10.1159/000506741}}

In case you are interested: My ORCID identifier is 0000-0002-7224-187X and here is a link to my arxiv author page (where you can find some of the articles listed above).