HOD and Higher Descriptive Set Theory
HOD and Higher Descriptive Set Theory
Sy-David Friedman
(ORCID: 0000-0001-8460-4394)
Disciplines
Mathematics (100%)
Keywords
-
Large Cardinals,
Ordinal Definability,
Borel sets
Mathematical logic entered the modern era through the work of Kurt Gödel, who established his famous Completeness and Incompleteness Theorems in Vienna in the 1930`s. This project, to be based at the Kurt Gödel Resarch 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 topics are: large cardinals and combinatorial principles, the hereditarily ordinal definable sets and the descriptive set theory of the uncountable.
Mathematical logic entered the modern era through the work of Kurt Gödel, who established his famous Completeness and Incompleteness Theorems in Vienna in the 1930`s. This project, based at the Kurt Gödel Research Center for Mathematical Logic of the University of Vienna, focused on set theory, the area of logic that most interested Gödel in his later years. The researched topics were: large cardinals and combinatorial principles, the hereditarily ordinal definable sets and the descriptive set theory of the uncountable.
Research institution(s)
- Universität Wien - 100%
Research Output
- 105 Citations
- 31 Publications
Publications
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2017
Title Full-splitting Miller trees and infinitely often equal reals DOI 10.1016/j.apal.2017.02.001 Type Journal Article Author Khomskii Y Journal Annals of Pure and Applied Logic Pages 1491-1506 Link Publication -
2016
Title Collapsing the cardinals of HOD DOI 10.1142/s0219061315500075 Type Journal Article Author Cummings J Journal Journal of Mathematical Logic -
2016
Title Regularity properties on the generalized reals DOI 10.1016/j.apal.2016.01.001 Type Journal Article Author Friedman S Journal Annals of Pure and Applied Logic Pages 408-430 Link Publication -
2012
Title Conjectures of Rado and Chang and special Aronszajn trees DOI 10.1002/malq.201110037 Type Journal Article Author Todorcevic S Journal Mathematical Logic Quarterly Pages 342-347 -
2013
Title Slow consistency DOI 10.1016/j.apal.2012.11.009 Type Journal Article Author Friedman S Journal Annals of Pure and Applied Logic Pages 382-393 Link Publication -
2013
Title Projective Hausdorff gaps DOI 10.1007/s00153-013-0355-6 Type Journal Article Author Khomskii Y Journal Archive for Mathematical Logic Pages 57-64 -
2013
Title The Nonabsoluteness of Model Existence in Uncountable Cardinals for L?1,? DOI 10.1215/00294527-1960443 Type Journal Article Author Friedman S Journal Notre Dame Journal of Formal Logic Pages 137-151 Link Publication -
2013
Title Killing The GCH Everywhere with a Single Real DOI 10.2178/jsl.7803060 Type Journal Article Author Friedman S Journal The Journal of Symbolic Logic Pages 803-823 Link Publication -
2013
Title Mad Families Constructed from Perfect Almost Disjoint Families DOI 10.2178/jsl.7804070 Type Journal Article Author Brendle J Journal The Journal of Symbolic Logic Pages 1164-1180 -
2014
Title Large cardinals need not be large in HOD DOI 10.48550/arxiv.1407.6335 Type Other Author Cheng Y Link Publication -
2014
Title Cichon’s diagram, regularity properties and ?31 sets of reals DOI 10.1007/s00153-014-0385-8 Type Journal Article Author Fischer V Journal Archive for Mathematical Logic Pages 695-729 -
2014
Title Regularity Properties on the Generalized Reals DOI 10.48550/arxiv.1408.5582 Type Preprint Author Friedman S Link Publication -
2014
Title Cofinal maximal chains in the Turing degrees DOI 10.1090/s0002-9939-2014-11868-5 Type Journal Article Author Wang W Journal Proceedings of the American Mathematical Society Pages 1391-1398 Link Publication -
2014
Title On the separation of regularity properties of the reals DOI 10.1007/s00153-014-0386-7 Type Journal Article Author Laguzzi G Journal Archive for Mathematical Logic Pages 731-747 -
2014
Title Rank-into-rank hypotheses and the failure of GCH DOI 10.1007/s00153-014-0369-8 Type Journal Article Author Dimonte V Journal Archive for Mathematical Logic Pages 351-366 Link Publication -
2012
Title Independence of higher Kurepa hypotheses DOI 10.1007/s00153-012-0286-7 Type Journal Article Author Friedman S Journal Archive for Mathematical Logic Pages 621-633 Link Publication -
2013
Title Killing GCH everywhere by a cofinality-preserving forcing notion over a model of GCH. Type Journal Article Author Friedman S -
2013
Title Co-analytic mad families and definable wellorders DOI 10.1007/s00153-013-0345-8 Type Journal Article Author Fischer V Journal Archive for Mathematical Logic Pages 809-822 -
2013
Title Killing GCH everywhere by a cofinality-preserving forcing notion over a model of GCH DOI 10.4064/fm223-2-3 Type Journal Article Author Friedman S Journal Fundamenta Mathematicae -
2013
Title Subcompact cardinals, squares, and stationary reflection DOI 10.1007/s11856-013-0007-x Type Journal Article Author Brooke-Taylor A Journal Israel Journal of Mathematics Pages 453-473 Link Publication -
2014
Title Easton functions and supercompactness DOI 10.4064/fm226-3-6 Type Journal Article Author Cody B Journal Fundamenta Mathematicae Pages 279-296 Link Publication -
2014
Title Adding a lot of Cohen reals by adding a few. I DOI 10.1090/s0002-9947-2014-06009-1 Type Journal Article Author Gitik M Journal Transactions of the American Mathematical Society Pages 209-229 Link Publication -
2016
Title Collapsing the cardinals of $HOD$ DOI 10.48550/arxiv.1601.03482 Type Other Author Cummings J Link Publication -
2015
Title Killing GCH everywhere by a cofinality-preserving forcing notion over a model of GCH DOI 10.48550/arxiv.1510.02937 Type Other Author Friedman S Link Publication -
2015
Title The tree property at the ?2n's and the failure of SCH at ?? DOI 10.1016/j.apal.2014.11.009 Type Journal Article Author Friedman S Journal Annals of Pure and Applied Logic Pages 526-552 Link Publication -
2014
Title Some considerations on amoeba forcing notions DOI 10.1007/s00153-014-0375-x Type Journal Article Author Laguzzi G Journal Archive for Mathematical Logic Pages 487-502 Link Publication -
2015
Title ? 1 -Definability of the non-stationary ideal at successor cardinals DOI 10.4064/fm229-3-2 Type Journal Article Author Friedman S Journal Fundamenta Mathematicae Pages 231-254 -
2015
Title Strong Chang's Conjecture and the tree property at ?2 DOI 10.1016/j.topol.2015.05.061 Type Journal Article Author Torres-Pérez V Journal Topology and its Applications Pages 999-1004 Link Publication -
2015
Title Large cardinals need not be large in HOD DOI 10.1016/j.apal.2015.07.004 Type Journal Article Author Cheng Y Journal Annals of Pure and Applied Logic Pages 1186-1198 Link Publication -
2015
Title Definable normal measures DOI 10.1016/j.apal.2014.09.001 Type Journal Article Author Friedman S Journal Annals of Pure and Applied Logic Pages 46-60 Link Publication -
2003
Title Additivity properties of topological diagonalizations DOI 10.2178/jsl/1067620185 Type Journal Article Author Bartoszynski T Journal Journal of Symbolic Logic Pages 1254-1260 Link Publication