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Contributions to the Metamathematics of Arithmetic: Fixed Points, Independence, and Flexibility


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Title: Contributions to the Metamathematics of Arithmetic: Fixed Points, Independence, and Flexibility
Authors: Blanck, Rasmus
Issue Date: 11-May-2017
University: 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
Date of Defence: 2017-06-02
Disputation: Fredagen den 2 juni 2017, kl. 9.00, sal T302, Gamla Hovrätten, Olof Wijksgatan 6
Degree: Doctor of Philosophy
Publication type: Doctoral thesis
Series/Report no.: Acta Philosophica Gothoburgensia
30
Keywords: arithmetic
incompleteness
flexibility
independence
non-standard models
partial conservativity
interpretability
Abstract: This thesis concerns the incompleteness phenomenon of first-order arithmetic: no consistent, r.e. theory T can prove every true arithmetical sentence. The first incompleteness result is due to Gödel; classic generalisations are due to Rosser, Feferman, Mostowski, and Kripke. All these results can be proved using self-referential statements in the form of provable fixed points. Chapter 3 studies sets of fixed points; the main result is that disjoint such sets are creative. Hierarchical generalisa... more
ISBN: 978-91-7346-917-3 (print)
978-91-7346-918-0 (pdf)
ISSN: 0283-2380
URI: http://hdl.handle.net/2077/52271
Appears in Collections:Doctoral Theses from University of Gothenburg / Doktorsavhandlingar från Göteborgs universitet
Doctoral Theses / Doktorsavhandlingar Institutionen för filosofi, lingvistik och vetenskapsteori

 

 

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