The Hyperuniverse Programme
The Hyperuniverse Programme
Sy-David Friedman
(ORCID: 0000-0001-8460-4394)
Disciplines
Mathematics (50%); Philosophy, Ethics, Religion (50%)
Keywords
-
Truth,
Intrinsic Evidence,
Hyperuniverse,
Maximality
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 the philosophy of set theory, a topic which interested Gödel throughout his career. The proposed topic is "The Hyperuniverse Programme", a new approach to truth in set theory based on maximality, an intrinsic feature of the universe of sets.
This project studied both mathematical and philosophical aspects of the foundations of set theory. We explored how background ontology affects the meaning of "maximality" in set theory and showed that the universe of sets can be described using the method of forcing and the theory of iteration from large cardinal theory. Our work was carried out at the Kurt Goedel Research Center through the efforts of two postdocs together with the project leader.
Research institution(s)
- Universität Wien - 100%
International project participants
- Oystein Linnebo, IFIKK - Norway
- Justin T. Moore, Cornell University - USA
- Peter Koellner, Harvard University - USA
- William Hugh Woodin, Harvard University - USA
- Paul Larson, University of Miami - USA
- Geoffrey Hellman, University of Minnesota at Minneapolis St. Paul - USA
Research Output
- 73 Citations
- 41 Publications
Publications
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2024
Title Mutually embeddable models of ZFC DOI 10.1016/j.apal.2023.103325 Type Journal Article Author Eskew M Journal Annals of Pure and Applied Logic Pages 103325 Link Publication -
2019
Title Introduction DOI 10.1007/s11229-019-02422-3 Type Journal Article Author Antos C Journal Synthese -
2019
Title Structural Properties of the Stable Core DOI 10.48550/arxiv.1910.02265 Type Preprint Author Friedman S Link Publication -
2019
Title Embeddings into outer models DOI 10.48550/arxiv.1905.06062 Type Other Author Eskew M 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 -
2022
Title EMBEDDINGS INTO OUTER MODELS DOI 10.1017/jsl.2022.52 Type Journal Article Author Eskew M Journal The Journal of Symbolic Logic Pages 1301-1321 Link Publication -
2019
Title Absence perception and the philosophy of zero DOI 10.1007/s11229-019-02220-x Type Journal Article Author Barton N Journal Synthese Pages 3823-3850 Link Publication -
2019
Title GENERIC LARGE CARDINALS AS AXIOMS DOI 10.1017/s1755020319000200 Type Journal Article Author Eskew M Journal The Review of Symbolic Logic Pages 375-387 Link Publication -
2019
Title More rigid ideals DOI 10.1007/s11856-019-1905-3 Type Journal Article Author Eskew M Journal Israel Journal of Mathematics Pages 225-247 -
2018
Title Global Chang's Conjecture and singular cardinals DOI 10.48550/arxiv.1812.11768 Type Preprint Author Eskew M Link Publication -
2020
Title Integration with filters DOI 10.48550/arxiv.2004.09103 Type Preprint Author Bottazzi E Link Publication -
2020
Title On a strengthening of Jónssonness for ?? DOI 10.1002/malq.201900073 Type Journal Article Author Eskew M Journal Mathematical Logic Quarterly Pages 235-238 Link Publication -
2020
Title UNIVERSISM AND EXTENSIONS OF V DOI 10.1017/s1755020320000271 Type Journal Article Author Antos C Journal The Review of Symbolic Logic Pages 112-154 Link Publication -
2020
Title Local saturation and square everywhere DOI 10.1142/s0219061320500191 Type Journal Article Author Eskew M Journal Journal of Mathematical Logic Pages 2050019 Link Publication -
2020
Title Maximality Principles in the Hyperuniverse Programme DOI 10.1007/s10699-020-09707-8 Type Journal Article Author Friedman S Journal Foundations of Science Pages 1-19 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 -
2021
Title Nonregular ideals DOI 10.4064/fm960-9-2020 Type Journal Article Author Eskew M Journal Fundamenta Mathematicae Pages 121-131 -
2021
Title Global Chang’s Conjecture and singular cardinals DOI 10.1007/s40879-021-00459-8 Type Journal Article Author Eskew M Journal European Journal of Mathematics Pages 435-463 Link Publication -
2020
Title Erratum for “On the consistency of local and global versions of Chang’s Conjecture” DOI 10.1090/tran/8171 Type Journal Article Author Eskew M Journal Transactions of the American Mathematical Society Pages 753-753 Link Publication -
2021
Title Ideal Topologies in Higher Descriptive Set Theory DOI 10.48550/arxiv.2111.07339 Type Preprint Author Holy P -
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 -
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 -
2021
Title Mutually embeddable models of ZFC DOI 10.48550/arxiv.2108.12355 Type Preprint Author Eskew M -
2018
Title Strongly proper forcing and some problems of Foreman DOI 10.1090/tran/7725 Type Journal Article Author Cox S Journal Transactions of the American Mathematical Society Pages 5039-5068 Link Publication -
2018
Title Rigid ideals DOI 10.1007/s11856-018-1650-z Type Journal Article Author Cody B Journal Israel Journal of Mathematics Pages 343-366 -
2016
Title Multiversism and Concepts of Set: How Much Relativism Is Acceptable? DOI 10.1007/978-3-319-31644-4_11 Type Book Chapter Author Barton N Publisher Springer Nature Pages 189-209 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 -
2017
Title On the consistency of local and global versions of Chang’s Conjecture DOI 10.1090/tran/7260 Type Journal Article Author Eskew M Journal Transactions of the American Mathematical Society Pages 2879-2905 Link Publication -
2017
Title Evidence for Set-Theoretic Truth and the Hyperuniverse Programme DOI 10.1007/978-3-319-62935-3_4 Type Book Chapter Author Friedman S Publisher Springer Nature Pages 75-107 -
2017
Title Maximality and ontology: how axiom content varies across philosophical frameworks DOI 10.1007/s11229-017-1336-9 Type Journal Article Author Barton N Journal Synthese Pages 623-649 Link Publication -
2017
Title Independence and Ignorance: How Agnotology Informs Set-Theoretic Pluralism DOI 10.1007/s40961-017-0102-1 Type Journal Article Author Barton N Journal Journal of Indian Council of Philosophical Research Pages 399-413 Link Publication -
2019
Title Set Theory and Structures DOI 10.1007/978-3-030-15655-8_10 Type Book Chapter Author Barton N Publisher Springer Nature Pages 223-253 Link Publication -
2019
Title Forcing and the Universe of Sets: Must We Lose Insight? DOI 10.1007/s10992-019-09530-y Type Journal Article Author Barton N Journal Journal of Philosophical Logic Pages 575-612 Link Publication -
2019
Title A model of second-order arithmetic satisfying AC but not DC DOI 10.1142/s0219061318500137 Type Journal Article Author Friedman S Journal Journal of Mathematical Logic Pages 1850013 Link Publication -
2019
Title Inner-Model Reflection Principles DOI 10.1007/s11225-019-09860-7 Type Journal Article Author Barton N Journal Studia Logica Pages 573-595 Link Publication -
2017
Title HYPERCLASS FORCING IN MORSE-KELLEY CLASS THEORY DOI 10.1017/jsl.2016.74 Type Journal Article Author Antos C Journal The Journal of Symbolic Logic Pages 549-575 Link Publication -
2017
Title ON THE SET-GENERIC MULTIVERSE DOI 10.1142/9789813223523_0003 Type Book Chapter Author Friedman S Publisher World Scientific Publishing Pages 25-44 -
2017
Title Universism and Extensions of V DOI 10.48550/arxiv.1708.05751 Type Other Author Antos C Link Publication -
2017
Title On the Set-Generic Multiverse DOI 10.1007/978-3-319-62935-3_5 Type Book Chapter Author Friedman S Publisher Springer Nature Pages 109-124 -
2017
Title Inner-model reflection principles DOI 10.48550/arxiv.1708.06669 Type Other Author Barton N Link Publication -
2015
Title Richness and Reflection DOI 10.1093/philmat/nkv036 Type Journal Article Author Barton N Journal Philosophia Mathematica Pages 330-359