<div class="csl-bib-body">
<div class="csl-entry">Schlutzenberg, F. S. (2024, June 28). <i>Ladder mice</i> [Conference Presentation]. Determinacy, Inner Models and Forcing Axioms (Workshop), Wien, Austria.</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/209409
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dc.description.abstract
We will discuss a new analysis of ladder mice, first introduced and studied by Rudominer, and then Woodin and Steel. Our analysis establishes a (lightface) mouse set theorem, which appears to be more general than what was known earlier: OD_{alpha n} is a mouse set for every ordinal alpha of countable L(R)-cofinality such that [alpha,alpha] is a projective-like gap and alpha is not the successor of a strong gap, and for every integer n>=1. The analysis also gives an alternate proof of this in the case "just past projective", avoiding the stationary tower. It also establishes an associated on-a-cone "anti-correctness" result. Anti-correctness is the generalization of, for example, the facts that (Pi^1_3)^V truth about reals in M_1 is (Sigma^1_3)^{M_1}, and that (Pi^1_3)^{M_1} truth (about reals in M_1) is (Sigma^1_3)^V. Time permitting, we may also mention a version of ladder mice at the end of a weak gap / successor of a strong gap. This work appears to be a useful component toward a positive resolution of the Rudominer-Steel conjecture on optimal wellorders of the reals, a related question on which the author and Steel are working.
en
dc.language.iso
en
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dc.subject
Ladder mice
en
dc.subject
mouse set theorem
en
dc.subject
𝐿(ℝ)
en
dc.subject
anti-correctness
en
dc.title
Ladder mice
en
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
Determinacy, Inner Models and Forcing Axioms (Workshop)
en
tuw.event.startdate
24-06-2024
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tuw.event.enddate
28-06-2024
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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
Wien
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tuw.event.country
AT
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tuw.event.institution
Universität Wien
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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
