<div class="csl-bib-body">
<div class="csl-entry">Müller, S. (2023). Determinacy Axioms and Large Cardinals. In M. K. Banerjee & V. S. Sreejith (Eds.), <i>Logic and Its Applications. ICLA 2023</i> (pp. 68–78). https://doi.org/10.1007/978-3-031-26689-8_5</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/192707
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dc.description.abstract
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. This article outlines the main concepts and results connecting determinacy hypotheses with the existence of mice with large cardinals as well as recent progress in the area.
en
dc.description.sponsorship
FWF - Österr. Wissenschaftsfonds
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dc.description.sponsorship
FWF - Österr. Wissenschaftsfonds
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dc.description.sponsorship
FWF - Österr. Wissenschaftsfonds
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dc.language.iso
en
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dc.relation.ispartofseries
Lecture Notes in Computer Science
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dc.subject
Determinacy
en
dc.subject
Infinite game
en
dc.subject
Large cardinal
en
dc.title
Determinacy Axioms and Large Cardinals
en
dc.type
Inproceedings
en
dc.type
Konferenzbeitrag
de
dc.contributor.editoraffiliation
University of North Texas
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dc.relation.isbn
978-3-031-26689-8
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dc.description.startpage
68
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dc.description.endpage
78
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dc.relation.grantno
V 844-N
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dc.relation.grantno
Y1498
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dc.relation.grantno
I6087-N
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dc.type.category
Full-Paper Contribution
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tuw.booktitle
Logic and Its Applications. ICLA 2023
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tuw.container.volume
13963
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tuw.peerreviewed
true
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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.project.title
Determiniertheit und Woodin Limes von Woodin Kardinalzahlen
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tuw.project.title
Klassifikation abgeleiteter Modelle der Determiniertheit
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tuw.researchTopic.id
A3
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tuw.researchTopic.name
Fundamental Mathematics Research
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tuw.researchTopic.value
100
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tuw.publication.orgunit
E104-08 - Forschungsbereich Mengenlehre
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tuw.publisher.doi
10.1007/978-3-031-26689-8_5
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dc.description.numberOfPages
11
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tuw.author.orcid
0000-0002-7224-187X
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tuw.editor.orcid
0000-0003-4379-4915
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tuw.event.name
10th Indian Conference on Logic and its Applications
en
tuw.event.startdate
03-03-2023
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tuw.event.enddate
05-03-2023
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tuw.event.online
Hybrid
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tuw.event.type
Event for scientific audience
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tuw.event.country
IN
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tuw.event.presenter
Müller, Sandra
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tuw.presentation.online
Online
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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.openairecristype
http://purl.org/coar/resource_type/c_5794
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item.openairetype
conference paper
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item.cerifentitytype
Publications
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item.fulltext
no Fulltext
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item.grantfulltext
none
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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