On Solovay's Theorem and a Proof of Arithmetical Completeness of a New Predicate Modal Logic

Simple item page
dc.contributor.advisorTourlakis, George
dc.contributor.advisorEdmonds, Jeffrey
dc.contributor.authorHao, Yunge
dc.date.accessioned2021-11-15T15:17:05Z
dc.date.available2021-11-15T15:17:05Z
dc.date.copyright2021-04
dc.date.issued2021-11-15
dc.date.updated2021-11-15T15:17:05Z
dc.degree.disciplineComputer Science
dc.degree.levelMaster's
dc.degree.nameMSc - Master of Science
dc.description.abstractThis thesis investigates a first-order extension of GL called ML3. We briefly discuss the latters properties and some of its toolbox: some metatheorems, the conservation theorem, and its semantic completeness (with respect to finite reverse wellfounded Kripke models). Applying the Solovay technique to those models the thesis establishes its main result, namely, that ML3 is arithmetically complete. As expanded below, ML3 is a first-order modal logic that along with its built-in ability to simulate general classical first-order provability having simulate the metamathematical classical is also arithmetically complete in the Solovay sense. We also carefully reconstruct the proof of Solovays Lemmata in our Appendixes, including a complete mathematically rigorous construction of his graph-walking function h.
dc.identifier.urihttp://hdl.handle.net/10315/38649
dc.languageen
dc.rightsAuthor owns copyright, except where explicitly noted. Please contact the author directly with licensing requests.
dc.subjectTheoretical mathematics
dc.subject.keywordsmodal logic
dc.subject.keywordsKripke models
dc.subject.keywordsSolovay's theorem
dc.subject.keywordscomputability
dc.subject.keywordscompleteness
dc.subject.keywordsarithmetic
dc.subject.keywordssemantic
dc.subject.keywordsrecursion theorem
dc.titleOn Solovay's Theorem and a Proof of Arithmetical Completeness of a New Predicate Modal Logic
dc.typeElectronic Thesis or Dissertation

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Hao_Yunge_2021_Masters.pdf
Size:
890.68 KB
Format:
Adobe Portable Document Format
Description:
Download
License bundle
Now showing 1 - 2 of 2
No Thumbnail Available
Name:
license.txt
Size:
1.87 KB
Format:
Plain Text
Description:
Download
No Thumbnail Available
Name:
YorkU_ETDlicense.txt
Size:
3.39 KB
Format:
Plain Text
Description:
Download

Collections

Computer Science

All items in the YorkSpace institutional repository are protected by copyright, with all rights reserved except where explicitly noted.