Publikation: Recognizable sets and Woodin cardinals : Computation beyond the constructible universe
Dateien
Datum
Autor:innen
Herausgeber:innen
ISSN der Zeitschrift
Electronic ISSN
ISBN
Bibliografische Daten
Verlag
Schriftenreihe
Auflagebezeichnung
DOI (zitierfähiger Link)
ArXiv-ID
Internationale Patentnummer
Angaben zur Forschungsförderung
Projekt
Open Access-Veröffentlichung
Sammlungen
Core Facility der Universität Konstanz
Titel in einer weiteren Sprache
Publikationstyp
Publikationsstatus
Erschienen in
Zusammenfassung
We call a subset of an ordinal λrecognizableif it is the unique subset xof λfor which some Turing machine with ordinal time and tape and an ordinal parameter, that halts for all subsets of λas input, halts with the final state 0. Equivalently, such a set is the unique subset xwhich satisfies a given Σ1formula in L[x]. We further define the recognizable closurefor subsets of λ by closing under relative recognizability for subsets of λ.
We prove several results about recognizable sets and their variants for other types of machines. Notably, we show the following results from large cardinals.
•Recognizable sets of ordinals appear in the hierarchy of inner models at least up to the level Woodin cardinals, while computable sets are elements of L.
•A subset of a countable ordinal λis in the recognizable closure for subsets of countable ordinals if and only if it is an element of the inner model M∞, which is obtained by iterating the least measure of the least fine structural inner model M1with a Woodin cardinal through the ordinals.
Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
Schlagwörter
Konferenz
Rezension
Zitieren
ISO 690
CARL, Merlin, Philipp SCHLICHT, Philip WELCH, 2018. Recognizable sets and Woodin cardinals : Computation beyond the constructible universe. In: Annals of Pure and Applied Logic. 2018, 169(4), pp. 312-332. ISSN 0168-0072. eISSN 1873-2461. Available under: doi: 10.1016/j.apal.2017.12.007BibTex
@article{Carl2018Recog-32698.2, year={2018}, doi={10.1016/j.apal.2017.12.007}, title={Recognizable sets and Woodin cardinals : Computation beyond the constructible universe}, number={4}, volume={169}, issn={0168-0072}, journal={Annals of Pure and Applied Logic}, pages={312--332}, author={Carl, Merlin and Schlicht, Philipp and Welch, Philip} }
RDF
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#" xmlns:foaf="http://xmlns.com/foaf/0.1/" xmlns:void="http://rdfs.org/ns/void#" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/32698.2"> <dc:contributor>Carl, Merlin</dc:contributor> <foaf:homepage rdf:resource="http://localhost:8080/"/> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dc:creator>Schlicht, Philipp</dc:creator> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2018-02-05T13:41:57Z</dcterms:available> <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/> <dcterms:title>Recognizable sets and Woodin cardinals : Computation beyond the constructible universe</dcterms:title> <dcterms:issued>2018</dcterms:issued> <dc:language>eng</dc:language> <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2018-02-05T13:41:57Z</dc:date> <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/32698.2"/> <dc:creator>Welch, Philip</dc:creator> <dc:contributor>Schlicht, Philipp</dc:contributor> <dc:creator>Carl, Merlin</dc:creator> <dc:contributor>Welch, Philip</dc:contributor> <dcterms:abstract xml:lang="eng">We call a subset of an ordinal λrecognizableif it is the unique subset xof λfor which some Turing machine with ordinal time and tape and an ordinal parameter, that halts for all subsets of λas input, halts with the final state 0. Equivalently, such a set is the unique subset xwhich satisfies a given Σ<sub>1</sub>formula in L[x]. We further define the recognizable closurefor subsets of λ by closing under relative recognizability for subsets of λ.<br /><br /><br />We prove several results about recognizable sets and their variants for other types of machines. Notably, we show the following results from large cardinals.<br /><br />•Recognizable sets of ordinals appear in the hierarchy of inner models at least up to the level Woodin cardinals, while computable sets are elements of L.<br /><br />•A subset of a countable ordinal λis in the recognizable closure for subsets of countable ordinals if and only if it is an element of the inner model M<sup>∞</sup>, which is obtained by iterating the least measure of the least fine structural inner model M<sub>1</sub>with a Woodin cardinal through the ordinals.</dcterms:abstract> </rdf:Description> </rdf:RDF>