• Skip to content (access key 1)
  • Skip to search (access key 7)
FWF — Austrian Science Fund
  • Go to overview page Discover

    • Research Radar
    • Discoveries
      • Emmanuelle Charpentier
      • Adrian Constantin
      • Monika Henzinger
      • Ferenc Krausz
      • Wolfgang Lutz
      • Walter Pohl
      • Christa Schleper
      • Anton Zeilinger
    • scilog Magazine
    • Awards
      • FWF Wittgenstein Awards
      • FWF START Awards
    • excellent=austria
      • Clusters of Excellence
      • Emerging Fields
    • In the Spotlight
      • 40 Years of Erwin Schrödinger Fellowships
      • Quantum Austria
    • Dialogs and Talks
      • think.beyond Summit
    • E-Book Library
  • Go to overview page Funding

    • Portfolio
      • excellent=austria
        • Clusters of Excellence
        • Emerging Fields
      • Projects
        • Principal Investigator Projects
        • Principal Investigator Projects International
        • Clinical Research
        • 1000 Ideas
        • Arts-Based Research
        • FWF Wittgenstein Award
      • Careers
        • ESPRIT
        • FWF ASTRA Awards
        • Erwin Schrödinger
        • Elise Richter
        • Elise Richter PEEK
        • doc.funds
        • doc.funds.connect
      • Collaborations
        • Specialized Research Groups
        • Special Research Areas
        • Research Groups
        • International – Multilateral Initiatives
        • #ConnectingMinds
      • Communication
        • Top Citizen Science
        • Science Communication
        • Book Publications
        • Digital Publications
        • Open-Access Block Grant
      • Subject-Specific Funding
        • AI Mission Austria
        • Belmont Forum
        • ERA-NET HERA
        • ERA-NET NORFACE
        • ERA-NET QuantERA
        • ERA-NET TRANSCAN
        • Alternative Methods to Animal Testing
        • European Partnership Biodiversa+
        • European Partnership ERA4Health
        • European Partnership ERDERA
        • European Partnership EUPAHW
        • European Partnership FutureFoodS
        • European Partnership OHAMR
        • European Partnership PerMed
        • European Partnership Water4All
        • Gottfried and Vera Weiss Award
        • netidee SCIENCE
        • Herzfelder Foundation Projects
        • Quantum Austria
        • Rückenwind Funding Bonus
        • Zero Emissions Award
      • International Collaborations
        • Belgium/Flanders
        • Germany
        • France
        • Italy/South Tyrol
        • Japan
        • Luxembourg
        • Poland
        • Switzerland
        • Slovenia
        • Taiwan
        • Tyrol–South Tyrol–Trentino
        • Czech Republic
        • Hungary
    • Step by Step
      • Find Funding
      • Submitting Your Application
      • International Peer Review
      • Funding Decisions
      • Carrying out Your Project
      • Closing Your Project
      • Further Information
        • Integrity and Ethics
        • Inclusion
        • Applying from Abroad
        • Personnel Costs
        • PROFI
        • Final Project Reports
        • Final Project Report Survey
    • FAQ
      • Project Phase PROFI
        • Accounting for Approved Funds
        • Labor and Social Law
        • Project Management
      • Project Phase Ad Personam
        • Accounting for Approved Funds
        • Labor and Social Law
        • Project Management
      • Expiring Programs
        • FWF START Awards
  • Go to overview page About Us

    • Mission Statement
    • FWF Video
    • Values
    • Facts and Figures
    • Annual Report
    • What We Do
      • Research Funding
        • Matching Funds Initiative
      • International Collaborations
      • Studies and Publications
      • Equal Opportunities and Diversity
        • Objectives and Principles
        • Measures
        • Creating Awareness of Bias in the Review Process
        • Terms and Definitions
        • Your Career in Cutting-Edge Research
      • Open Science
        • Open Access Policy
          • Open Access Policy for Peer-Reviewed Publications
          • Open Access Policy for Peer-Reviewed Book Publications
          • Open Access Policy for Research Data
        • Research Data Management
        • Citizen Science
        • Open Science Infrastructures
        • Open Science Funding
      • Evaluations and Quality Assurance
      • Academic Integrity
      • Science Communication
      • Philanthropy
      • Sustainability
    • History
    • Legal Basis
    • Organization
      • Executive Bodies
        • Executive Board
        • Supervisory Board
        • Assembly of Delegates
        • Scientific Board
        • Juries
      • FWF Office
    • Jobs at FWF
  • Go to overview page News

    • News
    • Press
      • Logos
    • Calendar
      • Post an Event
      • FWF Informational Events
    • Job Openings
      • Enter Job Opening
    • Newsletter
  • Discovering
    what
    matters.

    FWF-Newsletter Press-Newsletter Calendar-Newsletter Job-Newsletter scilog-Newsletter

    SOCIAL MEDIA

    • LinkedIn, external URL, opens in a new window
    • Twitter, external URL, opens in a new window
    • Facebook, external URL, opens in a new window
    • Instagram, external URL, opens in a new window
    • YouTube, external URL, opens in a new window

    SCILOG

    • Scilog — The science magazine of the Austrian Science Fund (FWF)
  • elane login, external URL, opens in a new window
  • Scilog external URL, opens in a new window
  • de Wechsle zu Deutsch

  

Generic large cardinals and determinacy

Generic large cardinals and determinacy

Monroe Blake Eskew (ORCID: 0000-0001-8094-9731)
  • Grant DOI 10.55776/PIN1355423
  • Funding program Principal Investigator Projects International
  • Status ongoing
  • Start August 1, 2024
  • End July 31, 2027
  • Funding amount € 679,003
  • Project website
  • E-mail

Weave: Österreich - Belgien - Deutschland - Luxemburg - Polen - Schweiz - Slowenien - Tschechien

Disciplines

Mathematics (100%)

Keywords

    Dense Ideals, Determinacy, Set Theory, Relative Consistency, Large Cardinals, Forcing

Abstract

Set theory is the mathematical study of infinity and has been very successful both in answering its own deep fundamental questions and in being applied elsewhere. Gödels Program is a major set theoretic undertaking addressing the most fundamental set theoretic issue: the fact that many basic questions about infinite sets are not decided by the standard axiom system ZFC. One important aspect of Gödels Program is to investigate theories of high logical strength that may disagree with each other on some set theoretic questions but can be seen as different aspects of the same endeavor through their mutual interpretability. In this project, our goal is to establish bridges between two such theories: generic large cardinals and strong forms of the Axiom of Determinacy. One of the prime objectives of this project is the construction of dense ideals on the first omega uncountable cardinals. We aim to construct such ideals using Cohens method of forcing over both models of determinacy as well as models of traditional large cardinals, which will show that the theory of dense ideals can be interpreted by two different foundational frameworks. Such ideals have already been constructed on the first two uncountable cardinals, but the construction of such ideals on higher cardinals has been a major open problem in set theory. The existence of such ideals has number of applications in infinitary combinatorics, model theory, and algebra. We also aim to calibrate the exact consistency strength of the theory asserting the existence of such ideals by constructing models of determinacy from such ideals, providing the desired mutual interpretation. We expect this project to be highly innovative, as the potential connections between determinacy and dense ideals above the first uncountable cardinal have not yet been explored. Our methods will involve innovations in forcing technology, both in the classical context of ZFC with large cardinals, as well as in the more bespoke context of forcing over models of determinacy. Our consistency calibration pushes against recently-discovered limitations of the core model induction, and thus should lead to breakthroughs in this methodology.

Research institution(s)
  • Universität Wien - 100%
International project participants
  • Yair Hayut, Hebrew University Jerusalem - Israel
  • Grigor Sargsyan, Polish Academy of Sciences - Poland, international project partner

Discovering
what
matters.

Newsletter

FWF-Newsletter Press-Newsletter Calendar-Newsletter Job-Newsletter scilog-Newsletter

Contact

Austrian Science Fund (FWF)
Georg-Coch-Platz 2
(Entrance Wiesingerstraße 4)
1010 Vienna

office(at)fwf.ac.at
+43 1 505 67 40

General information

  • Job Openings
  • Jobs at FWF
  • Press
  • Philanthropy
  • scilog
  • FWF Office
  • Social Media Directory
  • LinkedIn, external URL, opens in a new window
  • Twitter, external URL, opens in a new window
  • Facebook, external URL, opens in a new window
  • Instagram, external URL, opens in a new window
  • YouTube, external URL, opens in a new window
  • Cookies
  • Whistleblowing/Complaints Management
  • Accessibility Statement
  • Data Protection
  • Acknowledgements
  • Social Media Directory
  • © Österreichischer Wissenschaftsfonds FWF
© Österreichischer Wissenschaftsfonds FWF