Infinitary Combinatorics and Definability
Infinitary Combinatorics and Definability
Vera Fischer
(ORCID: 0000-0002-4710-8241)
Disciplines
Mathematics (100%)
Keywords
-
Real Line,
Cardinal Characteristics,
Forcing,
Definability,
Independence,
Large Continuum
The combinatorial properties of infinite sets of reals have been of interest since the early development of analysis in the 19th century. It can even be said that the work of Georg Cantor from 1872 on the trigonometric series representation of a function marks the very beginning of the subject of Set Theory. Two ground-breaking developments in this subject are the appearance of Kurt Gödel`s Constructible Universe and Paul Cohen`s method of Forcing. The current project focusses on some of the central problems of the infinitary combinatorial properties of the real line, arising from the above two phenomenon, definability and independence.
Research institution(s)
- Universität Wien - 100%
International project participants
- Juris Steprans, University of York - Canada
- Ansger Törnquist, University of Copenhagen - Denmark
- Heike Mildenberger, Albert-Ludwigs-Universität Freiburg - Germany
- Jörg Brendle, Kobe University - Japan
- Diego Mejia, Shizuoka University - Japan
- Michael Hrusak, Universidad Nacional Autonoma de Mexico - Mexico
- Andrew Brooke-Taylor, University of Leeds - United Kingdom
Research Output
- 27 Citations
- 41 Publications
Publications
-
2021
Title A Sacks indestructible co-analytic maximal eventually different family DOI 10.4064/fm842-1-2020 Type Journal Article Author Fischer V Journal Fundamenta Mathematicae Pages 179-201 Link Publication -
2021
Title Coanalytic ultrafilter bases DOI 10.1007/s00153-021-00801-7 Type Journal Article Author Schilhan J Journal Archive for Mathematical Logic Pages 567-581 -
2022
Title The structure of ?-maximal cofinitary groups DOI 10.1007/s00153-022-00859-x Type Journal Article Author Fischer V Journal Archive for Mathematical Logic Pages 641-655 Link Publication -
2022
Title Higher dimensional cardinal characteristics for sets of functions DOI 10.1016/j.apal.2021.103031 Type Journal Article Author Switzer C Journal Annals of Pure and Applied Logic Pages 103031 Link Publication -
2022
Title Integration with filters DOI 10.4115/jla.2022.14.1 Type Journal Article Author Bottazzi E Journal Journal of Logic and Analysis Link Publication -
2022
Title Ideal topologies in higher descriptive set theory DOI 10.1016/j.apal.2021.103061 Type Journal Article Author Holy P Journal Annals of Pure and Applied Logic Pages 103061 Link Publication -
2023
Title The special tree number DOI 10.4064/fm180-1-2023 Type Journal Article Author Switzer C Journal Fundamenta Mathematicae Pages 129-151 -
2023
Title TIGHT EVENTUALLY DIFFERENT FAMILIES DOI 10.1017/jsl.2023.9 Type Journal Article Author Fischer V Journal The Journal of Symbolic Logic Pages 697-723 Link Publication -
2023
Title CONSTRUCTING MAXIMAL COFINITARY GROUPS DOI 10.1017/nmj.2022.46 Type Journal Article Author Schrittesser D Journal Nagoya Mathematical Journal Pages 622-651 Link Publication -
2022
Title Towers and gaps at uncountable cardinals DOI 10.4064/fm109-9-2021 Type Journal Article Author Fischer V Journal Fundamenta Mathematicae Pages 141-166 Link Publication -
2022
Title HIGHER INDEPENDENCE DOI 10.1017/jsl.2022.33 Type Journal Article Author Fischer V Journal The Journal of Symbolic Logic Pages 1606-1630 Link Publication -
2022
Title Projective well orders and coanalytic witnesses DOI 10.1016/j.apal.2022.103135 Type Journal Article Author Bergfalk J Journal Annals of Pure and Applied Logic Pages 103135 Link Publication -
2022
Title TREE FORCING AND DEFINABLE MAXIMAL INDEPENDENT SETS IN HYPERGRAPHS DOI 10.1017/jsl.2022.36 Type Journal Article Author Schilhan J Journal The Journal of Symbolic Logic Pages 1419-1458 Link Publication -
2022
Title The spectrum of independence, II DOI 10.1016/j.apal.2022.103161 Type Journal Article Author Fischer V Journal Annals of Pure and Applied Logic Pages 103161 Link Publication -
2022
Title Filters and Ideal Independence DOI 10.48550/arxiv.2206.14019 Type Preprint Author Cancino-Manríquez J -
2022
Title Some combinatorial properties of splitting trees DOI 10.4064/ba210622-2-6 Type Journal Article Author Schilhan J Journal Bulletin of the Polish Academy of Sciences Mathematics Pages 1-12 Link Publication -
2022
Title The Special Tree Number DOI 10.48550/arxiv.2203.04186 Type Preprint Author Switzer C -
2022
Title Games on base matrices DOI 10.48550/arxiv.2203.02581 Type Preprint Author Fischer V -
2022
Title A descriptive approach to higher derived limits DOI 10.48550/arxiv.2203.00165 Type Preprint Author Bannister N -
2022
Title Destructibility and axiomatizability of Kaufmann models DOI 10.1007/s00153-022-00826-6 Type Journal Article Author Switzer C Journal Archive for Mathematical Logic Pages 1091-1111 Link Publication -
2023
Title Correction to: Towers, mad families, and unboundedness DOI 10.1007/s00153-023-00870-w Type Journal Article Author Fischer V Journal Archive for Mathematical Logic Pages 1159-1160 Link Publication -
2023
Title Separating Subversion Forcing Principles DOI 10.48550/arxiv.2308.16276 Type Preprint Author Sakai H -
2023
Title Generic Selective Independent Families DOI 10.48550/arxiv.2306.09809 Type Preprint Author Fischer V -
2023
Title Games on Base Matrices DOI 10.1215/00294527-10701451 Type Journal Article Author Fischer V Journal Notre Dame Journal of Formal Logic -
2023
Title Cohen preservation and independence DOI 10.1016/j.apal.2023.103291 Type Journal Article Author Fischer V Journal Annals of Pure and Applied Logic Pages 103291 Link Publication -
2021
Title Definable MAD families and forcing axioms DOI 10.1016/j.apal.2020.102909 Type Journal Article Author Fischer V Journal Annals of Pure and Applied Logic Pages 102909 Link Publication -
2021
Title Ideal Topologies in Higher Descriptive Set Theory DOI 10.48550/arxiv.2111.07339 Type Preprint Author Holy P -
2023
Title Strongly unfoldable, splitting and bounding DOI 10.1002/malq.202200003 Type Journal Article Author Bag Ö Journal Mathematical Logic Quarterly Pages 7-14 Link Publication -
2023
Title Fresh function spectra DOI 10.1016/j.apal.2023.103300 Type Journal Article Author Fischer V Journal Annals of Pure and Applied Logic Pages 103300 Link Publication -
2023
Title Towers, mad families, and unboundedness DOI 10.1007/s00153-023-00861-x Type Journal Article Author Fischer V Journal Archive for Mathematical Logic Pages 811-830 Link Publication -
2021
Title MORE ZFC INEQUALITIES BETWEEN CARDINAL INVARIANTS DOI 10.1017/jsl.2021.52 Type Journal Article Author Fischer V Journal The Journal of Symbolic Logic Pages 897-912 Link Publication -
2021
Title Constructing maximal cofinitary groups DOI 10.48550/arxiv.2105.11318 Type Preprint Author Schrittesser D -
2021
Title Tight Eventually Different Families DOI 10.48550/arxiv.2104.11291 Type Preprint Author Fischer V -
2021
Title Some combinatorial properties of splitting trees DOI 10.48550/arxiv.2106.07511 Type Preprint Author Schilhan J -
2022
Title PARTITION FORCING AND INDEPENDENT FAMILIES DOI 10.1017/jsl.2022.68 Type Journal Article Author Cruz-Chapital J Journal The Journal of Symbolic Logic Pages 1590-1612 Link Publication -
2022
Title Cohen Preservation and Independence DOI 10.48550/arxiv.2208.09854 Type Preprint Author Fischer V -
2022
Title HIGHER DIMENSIONAL CARDINAL CHARACTERISTICS FOR SETS OF FUNCTIONS II DOI 10.1017/jsl.2022.18 Type Journal Article Author Brendle J Journal The Journal of Symbolic Logic Pages 1421-1442 Link Publication -
2022
Title Definable towers DOI 10.4064/fm917-9-2021 Type Journal Article Author Fischer V Journal Fundamenta Mathematicae Pages 221-241 -
2022
Title Selective Independence and $h$-Perfect Tree Forcing Notions DOI 10.48550/arxiv.2202.12046 Type Preprint Author Switzer C -
2022
Title On heights of distributivity matrices DOI 10.48550/arxiv.2202.09255 Type Preprint Author Fischer V -
2020
Title THE POLARISED PARTITION RELATION FOR ORDER TYPES DOI 10.1093/qmathj/haaa003 Type Journal Article Author Klausner L Journal The Quarterly Journal of Mathematics Pages 823-842 Link Publication