<div class="csl-bib-body">
<div class="csl-entry">Schlutzenberg, F. S. (2024, February 8). <i>Σ1(X) and Π1(X) definability above large cardinals</i> [Conference Presentation]. Generalised Baire Space and Large Cardinals, Bristol, United Kingdom of Great Britain and Northern Ireland (the).</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/209408
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dc.description.abstract
I will talk about some results on the Sigma_1(X) and Pi_1(X) definability over H_{kappa^+} of pathological subsets of P(kappa), when there are large cardinals in V_kappa. In particular, if kappa is a limit of measurable cardinals then letting X=H_\kappa\cup OR, there is no Sigma_1(X) wellorder of a subset of P(\kappa) of length \geq\kappa^+, and there is no Sigma_1(X) mad family of cardinality >kappa. However, the existence of regular kappa with large cardinal properties together with Pi_1({kappa}) mad families and maximal independent families are consistent relative to large cardinals. And in M_1, the minimal proper class mouse with a Woodin cardinal, for every uncountable cardinal kappa which is not a limit of measurable cardinals, there
is a good Sigma_1(H_kappa\cup {kappa}) wellorder of H_{kappa^+}, where X is as before. Some of the results address questions of Lücke and Müller. Reference: "Low level definability above large cardinals".
en
dc.language.iso
en
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dc.subject
definability
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dc.subject
generalised descriptive set theory
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dc.subject
large cardinals
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dc.title
Σ1(X) and Π1(X) definability above large cardinals
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dc.type
Presentation
en
dc.type
Vortrag
de
dc.type.category
Conference Presentation
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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
E104-08 - Forschungsbereich Mengenlehre
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tuw.event.name
Generalised Baire Space and Large Cardinals
en
dc.description.sponsorshipexternal
FWF
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dc.relation.grantnoexternal
10.55776/Y1498
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tuw.event.startdate
08-02-2024
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tuw.event.enddate
10-02-2024
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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
Bristol
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tuw.event.country
GB
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tuw.event.institution
University of Bristol
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tuw.event.presenter
Schlutzenberg, Farmer Salamander
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tuw.event.track
Single Track
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wb.sciencebranch
Informatik
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wb.sciencebranch
Mathematik
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wb.sciencebranch.oefos
1020
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wb.sciencebranch.oefos
1010
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wb.sciencebranch.value
5
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wb.sciencebranch.value
95
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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.parentorg
E104 - Institut für Diskrete Mathematik und Geometrie
