dc.contributor.author | Kindvall Gorbow, Paul | |
dc.date.accessioned | 2018-05-24T09:30:23Z | |
dc.date.available | 2018-05-24T09:30:23Z | |
dc.date.issued | 2018-05-24 | |
dc.identifier.isbn | 978-91-7346-970-8 | |
dc.identifier.uri | http://hdl.handle.net/2077/56240 | |
dc.description.abstract | 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. | sv |
dc.language.iso | eng | sv |
dc.relation.ispartofseries | ACTA Philosophica Gothoburgensia | sv |
dc.relation.ispartofseries | 32 | sv |
dc.subject | Logic | sv |
dc.subject | Set theory | sv |
dc.subject | Category theory | sv |
dc.subject | Foundations of mathematics | sv |
dc.subject | Model theory | sv |
dc.subject | Categorical semantics | sv |
dc.subject | Algebraic set theory | sv |
dc.subject | Non-standard models | sv |
dc.title | Self-similarity in the foundations | sv |
dc.type | Text | |
dc.type.svep | Doctoral thesis | eng |
dc.type.degree | Doctor of Philosophy | sv |
dc.gup.origin | Göteborgs universitet. Humanistiska fakulteten | swe |
dc.gup.origin | University of Gothenburg. Faculty of Arts | eng |
dc.gup.department | Department of Philosophy, Linguistics and Theory of Science ; Institutionen för filosofi, lingvistik och vetenskapsteori | sv |
dc.gup.defenceplace | Torsdagen den 14 juni 2018, kl. 13, T302, Olof Wijksgatan 6, Göteborg. | sv |
dc.gup.defencedate | 2018-06-14 | |
dc.gup.dissdb-fakultet | HF | |