Set Theory: Dichotomies and definable wellorders
Set Theory: Dichotomies and definable wellorders
Sy-David Friedman
(ORCID: 0000-0001-8460-4394)
Disciplines
Mathematics (100%)
Keywords
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Dichotomies,
Cardinal Characteristics,
Definable Wellorders
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: dichotomy theorems in descriptive set theory, combinatorial consistency strengths, higher cardinal characteristics and definable wellorders.
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 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 topics are: dichotomy theorems in descriptive set theory, higher cardinal characteristics and definable wellorders.
Research institution(s)
- Universität Wien - 100%
Research Output
- 126 Citations
- 28 Publications
Publications
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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 -
2012
Title Equivalence Relations That Are Complete for Computable Reducibility DOI 10.1007/978-3-642-32621-9_2 Type Book Chapter Author Fokina E Publisher Springer Nature Pages 26-33 -
2012
Title Foundational implications of the Inner Model Hypothesis DOI 10.1016/j.apal.2012.01.009 Type Journal Article Author Arrigoni T Journal Annals of Pure and Applied Logic Pages 1360-1366 Link Publication -
2012
Title On Borel equivalence relations in generalized Baire space DOI 10.1007/s00153-011-0266-3 Type Journal Article Author Friedman S Journal Archive for Mathematical Logic Pages 299-304 Link Publication -
2012
Title A partially non-proper ordinal beyond L(V?+1) DOI 10.1016/j.apal.2012.02.003 Type Journal Article Author Dimonte V Journal Annals of Pure and Applied Logic Pages 1309-1321 Link Publication -
2013
Title The hyperuniverse program DOI 10.2178/bsl.1901030 Type Journal Article Author Arrigoni T Journal Bulletin of Symbolic Logic Pages 77-96 -
2013
Title The tree property at the double successor of a measurable cardinal ? with 2 ? large DOI 10.4064/fm223-1-4 Type Journal Article Author Friedman S Journal Fundamenta Mathematicae Pages 55-64 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 Fusion and large cardinal preservation DOI 10.1016/j.apal.2013.06.011 Type Journal Article Author Friedman S Journal Annals of Pure and Applied Logic Pages 1247-1273 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 -
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 -
2011
Title Condensation and large cardinals DOI 10.4064/fm215-2-3 Type Journal Article Author Friedman S Journal Fundamenta Mathematicae Pages 133-166 -
2015
Title Large cardinals and definable well-orders, without the GCH DOI 10.1016/j.apal.2014.11.003 Type Journal Article Author Friedman S Journal Annals of Pure and Applied Logic Pages 306-324 Link Publication -
2015
Title Forcing consequences of P F A PFA together with the continuum large DOI 10.1090/s0002-9947-2015-06205-9 Type Journal Article Author Asperó D Journal Transactions of the American Mathematical Society Pages 6103-6129 Link Publication -
2015
Title Killing the GCH everywhere with a single real DOI 10.48550/arxiv.1510.02933 Type Other Author Friedman S Link Publication -
2015
Title LARGE CARDINALS AND LIGHTFACE DEFINABLE WELL-ORDERS, WITHOUT THE GCH DOI 10.1017/jsl.2013.41 Type Journal Article Author Friedman S Journal The Journal of Symbolic Logic Pages 251-284 -
2015
Title The tree property at the successor and double successor of a singular cardinal. Type Journal Article Author Fontanella L -
2014
Title A quasi-lower bound on the consistency strength of PFA DOI 10.1090/s0002-9947-2014-05955-2 Type Journal Article Author Friedman S Journal Transactions of the American Mathematical Society Pages 4021-4065 Link Publication -
2015
Title Template iterations and maximal cofinitary groups DOI 10.4064/fm230-3-1 Type Journal Article Author Fischer V Journal Fundamenta Mathematicae Pages 205-236 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 A generalization of Martin's Axiom DOI 10.1007/s11856-015-1250-0 Type Journal Article Author Asperó D Journal Israel Journal of Mathematics -
2013
Title Cardinal characteristics, projective wellorders and large continuum DOI 10.1016/j.apal.2012.12.001 Type Journal Article Author Fischer V Journal Annals of Pure and Applied Logic Pages 763-770 Link Publication -
2012
Title Supercompactness and failures of GCH DOI 10.4064/fm219-1-2 Type Journal Article Author Friedman S Journal Fundamenta Mathematicae Pages 15-36 -
2012
Title Projective maximal families of orthogonal measures with large continuum DOI 10.4115/jla.2012.4.9 Type Journal Article Author Fischer Journal Journal of Logic and Analysis Pages 1-15 Link Publication -
2012
Title A Generalization of Martin's Axiom DOI 10.48550/arxiv.1206.6724 Type Preprint Author Asperó D Link Publication -
2012
Title Forcing consequences of PFA together with the continuum large DOI 10.48550/arxiv.1203.1235 Type Preprint Author Asperó D Link Publication -
2012
Title Measuring club-sequences with a large continuum DOI 10.48550/arxiv.1203.1238 Type Preprint Author Asperó D Link Publication -
0
Title A generalisation of Martin's Axiom. Type Other Author Aspero D