KOPS - Das Institutionelle Repositorium der Universität Konstanz

Recognizable sets and Woodin cardinals : Computation beyond the constructible universe

Recognizable sets and Woodin cardinals : Computation beyond the constructible universe

Zitieren

Dateien zu dieser Ressource

Dateien Größe Format Anzeige

Zu diesem Dokument gibt es keine Dateien.

CARL, Merlin, Philipp SCHLICHT, Philip WELCH, 2018. Recognizable sets and Woodin cardinals : Computation beyond the constructible universe. In: Annals of Pure and Applied Logic. 169(4), pp. 312-332. ISSN 0168-0072. eISSN 1873-2461. Available under: doi: 10.1016/j.apal.2017.12.007

@article{Carl2018Recog-32698.2, title={Recognizable sets and Woodin cardinals : Computation beyond the constructible universe}, year={2018}, doi={10.1016/j.apal.2017.12.007}, 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} }

Carl, Merlin Welch, Philip 2018 Carl, Merlin eng Schlicht, Philipp 2018-02-05T13:41:57Z 2018-02-05T13:41:57Z Welch, Philip 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. Recognizable sets and Woodin cardinals : Computation beyond the constructible universe Schlicht, Philipp

Das Dokument erscheint in:

Versionsgeschichte

Version Dokument Datum Zusammenfassung Publikationsstatus

* Ausgewählte Version

KOPS Suche


Stöbern

Mein Benutzerkonto