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  • Faculty of Humanities / Humanistiska fakulteten
  • Department of Philosophy, Linguistics and Theory of Science / Institutionen för filosofi, lingvistik och vetenskapsteori
  • Doctoral Theses / Doktorsavhandlingar Institutionen för filosofi, lingvistik och vetenskapsteori
  • Redigera dokument
  •   Startsida
  • Faculty of Humanities / Humanistiska fakulteten
  • Department of Philosophy, Linguistics and Theory of Science / Institutionen för filosofi, lingvistik och vetenskapsteori
  • Doctoral Theses / Doktorsavhandlingar Institutionen för filosofi, lingvistik och vetenskapsteori
  • Redigera dokument
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Self-similarity in the foundations

Sammanfattning
This thesis concerns embeddings and self-embeddings of foundational structures in both set theory and category theory. The first part of the work on models of set theory consists in establishing a refined version of Friedman's theorem on the existence of embeddings between countable non-standard models of a fragment of ZF, and an analogue of a theorem of Gaifman to the effect that certain countable models of set theory can be elementarily end-extended to a model with many automorphisms whose sets of fixed points equal the original model. The second part of the work on set theory consists in combining these two results into a technical machinery, yielding several results about non-standard models of set theory relating such notions as self-embeddings, their sets of fixed points, strong rank-cuts, and set theories of different strengths. The work in foundational category theory consists in the formulation of a novel algebraic set theory which is proved to be equiconsistent to New Foundations (NF), and which can be modulated to correspond to intuitionistic or classical NF, with or without atoms. A key axiom of this theory expresses that its structures have an endofunctor with natural properties.
Examinationsnivå
Doctor of Philosophy
Universitet
Göteborgs universitet. Humanistiska fakulteten
University of Gothenburg. Faculty of Arts
Institution
Department of Philosophy, Linguistics and Theory of Science ; Institutionen för filosofi, lingvistik och vetenskapsteori
Disputation
Torsdagen den 14 juni 2018, kl. 13, T302, Olof Wijksgatan 6, Göteborg.
Datum för disputation
2018-06-14
URL:
http://hdl.handle.net/2077/56240
Samlingar
  • Acta Philosophica Gothoburgensia
  • Doctoral Theses / Doktorsavhandlingar Institutionen för filosofi, lingvistik och vetenskapsteori
  • Doctoral Theses from University of Gothenburg / Doktorsavhandlingar från Göteborgs universitet
Fil(er)
Spikblad (67.37Kb)
Datum
2018-05-24
Författare
Kindvall Gorbow, Paul
Nyckelord
Logic
Set theory
Category theory
Foundations of mathematics
Model theory
Categorical semantics
Algebraic set theory
Non-standard models
Publikationstyp
Doctoral thesis
ISBN
978-91-7346-970-8
Serie/rapportnr.
ACTA Philosophica Gothoburgensia
32
Språk
eng
Metadata
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