<div class="csl-bib-body">
<div class="csl-entry">Müller, S. (2022, September). <i>Highlights from infinite games, mice and their connection.</i> [Conference Presentation]. PhDs in Logic XIII, Universität von Turin, Turin, Italy.</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/152849
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dc.description
Highlights from infinite games, mice, and their connection
The study of inner models was initiated by Gödel’s analysis of the constructible universe. Later, the study of canonical inner models with large cardinals, e.g., measurable cardinals, strong cardinals or Woodin cardinals, was pioneered by Jensen, Mitchell, Steel, and others. Around the same time, the study of infinite two-player games was driven forward by Martin’s proof of analytic determinacy from a measurable cardinal, Borel determinacy from ZFC, and Martin and Steel’s proof of levels of projective determinacy from Woodin cardinals with a measurable cardinal on top. First Woodin and later Neeman improved the result in the projective hierarchy by showing that in fact the existence of a countable iterable model, a mouse, with Woodin cardinals and a top measure suffices to prove determinacy in the projective hierarchy. This opened up the possibility for an optimal result stating the equivalence between local determinacy hypotheses and the existence of mice in the projective hierarchy. In this talk, we will outline the main concepts and results connecting determinacy hypotheses with the existence of mice with large cardinals as well as recent progress in the area.
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dc.description.sponsorship
Fonds zur Förderung der wissenschaftlichen Forschung (FWF)
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dc.language.iso
en
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dc.subject
The constructible universe
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dc.title
Highlights from infinite games, mice and their connection.
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dc.type
Presentation
en
dc.type
Vortrag
de
dc.relation.grantno
V 844_N
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dc.type.category
Conference Presentation
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tuw.publication.invited
invited
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tuw.project.title
Lange Spiele und Determiniertheit wenn alle Mengen uB sind
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tuw.researchTopic.id
C4
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tuw.researchTopic.name
Mathematical and Algorithmic Foundations
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tuw.researchTopic.value
100
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tuw.publication.orgunit
E104-01 - Forschungsbereich Algebra
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tuw.author.orcid
0000-0002-7224-187X
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tuw.event.name
PhDs in Logic XIII
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tuw.event.startdate
05-09-2022
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tuw.event.enddate
07-09-2022
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tuw.event.online
On Site
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tuw.event.type
Event for scientific audience
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tuw.event.place
Universität von Turin, Turin
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tuw.event.country
IT
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tuw.event.institution
Universität von Turin
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tuw.event.presenter
Müller, Sandra
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wb.sciencebranch
Mathematik
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wb.sciencebranch.oefos
1010
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wb.sciencebranch.value
100
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item.languageiso639-1
en
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item.openairetype
conference paper not in proceedings
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item.grantfulltext
none
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item.fulltext
no Fulltext
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item.cerifentitytype
Publications
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item.openairecristype
http://purl.org/coar/resource_type/c_18cp
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crisitem.author.dept
E104-08 - Forschungsbereich Mengenlehre
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crisitem.author.orcid
0000-0002-7224-187X
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crisitem.author.parentorg
E104 - Institut für Diskrete Mathematik und Geometrie
