Large Cardinals, Forcing and Determinacy
Large Cardinals, Forcing and Determinacy
Sy-David Friedman
(ORCID: 0000-0001-8460-4394)
Disciplines
Mathematics (100%)
Keywords
-
Large Cardinals,
Ideals,
Determinacy,
Projective Sets,
Regularity
Mathematical logic entered the modern era through the work of Kurt Gödel, who established his famous Completeness and Incompleteness Theorems in Vienna in the 1930s. This project, to be based at the Kurt Gödel Research Center for Mathematical Logic of the University of Vienna, focuses on set theory, the area of logic that most interested Gödel in his later years. The proposed topic is Large Cardinals, Forcing and Determinacy.
This project studied several aspects of modern set theory. We explored the axiom of determinacy, infinitary combinatorics, the Stable Core and generalisations of the Lebesgue Density Theorem. Our work was carried out at the Kurt Goedel Research Center through the efforts of three postdocs together with the project leader
Research institution(s)
- Universität Wien - 100%
International project participants
- Ralf Schindler, Universität Münster - Germany
- Masahiro Shioya, The University of Tsukuba - Japan
- John Steel, University of California Berkeley - USA
- Matthew D. Foreman, University of California Irvine - USA
- Martin Zeman, University of California at Irvine - USA
Research Output
- 43 Citations
- 21 Publications
Publications
-
2022
Title Lebesgue’s density theorem and definable selectors for ideals DOI 10.1007/s11856-022-2312-8 Type Journal Article Author Müller S Journal Israel Journal of Mathematics Pages 501-551 -
2022
Title CONSTRUCTING WADGE CLASSES DOI 10.1017/bsl.2022.7 Type Journal Article Author Carroy R Journal The Bulletin of Symbolic Logic Pages 207-257 Link Publication -
2021
Title IN INNER MODELS WITH WOODIN CARDINALS DOI 10.1017/jsl.2021.61 Type Journal Article Author Müller S Journal The Journal of Symbolic Logic Pages 871-896 Link Publication -
2020
Title GENERIC CODING WITH HELP AND AMALGAMATION FAILURE DOI 10.1017/jsl.2019.68 Type Journal Article Author Friedman S Journal The Journal of Symbolic Logic Pages 1385-1395 Link Publication -
2020
Title Projective Games on the Reals DOI 10.1215/00294527-2020-0027 Type Journal Article Author Aguilera J Journal Notre Dame Journal of Formal Logic -
2020
Title HOD in inner models with Woodin cardinals DOI 10.48550/arxiv.2004.09201 Type Preprint Author Müller S Link Publication -
2020
Title Every zero-dimensional homogeneous space is strongly homogeneous under determinacy DOI 10.1142/s0219061320500154 Type Journal Article Author Carroy R Journal Journal of Mathematical Logic Pages 2050015 Link Publication -
2023
Title STRUCTURAL PROPERTIES OF THE STABLE CORE DOI 10.1017/jsl.2023.10 Type Journal Article Author Friedman S Journal The Journal of Symbolic Logic Pages 889-918 Link Publication -
2019
Title THE CONSISTENCY STRENGTH OF LONG PROJECTIVE DETERMINACY DOI 10.1017/jsl.2019.78 Type Journal Article Author Aguilera J Journal The Journal of Symbolic Logic Pages 338-366 Link Publication -
2019
Title The semi-weak square principle DOI 10.1016/j.apal.2019.06.002 Type Journal Article Author Levine M Journal Annals of Pure and Applied Logic Pages 102713 -
2019
Title AN ANALYSIS OF THE MODELS DOI 10.1017/jsl.2016.63 Type Journal Article Author Atmai R Journal The Journal of Symbolic Logic Pages 1-26 -
2019
Title A WELLORDER OF THE REALS WITH SATURATED DOI 10.1017/jsl.2019.43 Type Journal Article Author Friedman S Journal The Journal of Symbolic Logic Pages 1466-1483 -
2018
Title Stationary sets added when forcing squares DOI 10.1007/s00153-018-0613-8 Type Journal Article Author Levine M Journal Archive for Mathematical Logic Pages 909-916 Link Publication -
2018
Title WEAK SQUARES AND VERY GOOD SCALES DOI 10.1017/jsl.2017.23 Type Journal Article Author Levine M Journal The Journal of Symbolic Logic Pages 1-12 -
2018
Title Lebesgue's Density Theorem and definable selectors for ideals DOI 10.48550/arxiv.1811.06489 Type Other Author Müller S Link Publication -
2020
Title Partitioning a reflecting stationary set DOI 10.1090/proc/14783 Type Journal Article Author Levine M Journal Proceedings of the American Mathematical Society Pages 3551-3565 Link Publication -
2019
Title Structural Properties of the Stable Core DOI 10.48550/arxiv.1910.02265 Type Preprint Author Friedman S Link Publication -
2019
Title Constructing Wadge classes DOI 10.48550/arxiv.1907.07612 Type Preprint Author Carroy R Link Publication -
2021
Title Squares and uncountably singularized cardinals DOI 10.4064/fm955-9-2020 Type Journal Article Author Levine M Journal Fundamenta Mathematicae Pages 277-296 -
2021
Title Long games and s-projective sets DOI 10.1016/j.apal.2020.102939 Type Journal Article Author Aguilera J Journal Annals of Pure and Applied Logic Pages 102939 Link Publication -
2018
Title THE EIGHTFOLD WAY DOI 10.1017/jsl.2017.69 Type Journal Article Author Cummings J Journal The Journal of Symbolic Logic Pages 349-371