Unfolding of systems of inductive definitions
Abstract/Contents
- Abstract
- This thesis is a contribution to Solomon Feferman's Unfolding Program which aims to provide a general method of capturing the operations on individuals and predicates (and the principles governing them) that are implicit in a formal axiomatic system based on open-ended schemata. The thesis in particular studies the unfolding of the classical system for one generalized positive arithmetical inductive definition. The main result is an ordinal analysis of this theory. The resulting ordinal has been known since Heinz Bachmann, and has been studied by Peter Aczel, who felt it should be of proof-theoretic interest. Solomon Feferman conjectured specifically that it should be the strength of the theory under consideration here, and this thesis verifies his conjecture. The upper bound proceeds via a system of numbers, inductive definitions and ordinals that is analyzed with a combination of operator-controlled derivations and asymmetric interpretation. The lower bound is established through a well-ordering proof that uses the unfolding machinery to construct hierarchies based on jump operators. This part highlights a new ingredient needed in the unfolding at this level, namely a dependent version of the join operator, producing disjoint unions of predicates indexed by a predicate. The thesis also includes an appendix detailing the history and motivation of the unfolding program, as well as an appendix describing previous work on the Aczel-Bachmann ordinal.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2013 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Buchholtz, Ulrik Torben |
|---|---|
| Associated with | Stanford University, Department of Mathematics. |
| Primary advisor | Feferman, Solomon |
| Primary advisor | Mint͡s, G. E |
| Thesis advisor | Feferman, Solomon |
| Thesis advisor | Mint͡s, G. E |
| Thesis advisor | Strahm, Thomas (Thomas Adrian) |
| Advisor | Strahm, Thomas (Thomas Adrian) |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Ulrik Torben Buchholtz. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Ph.D. Stanford University 2013. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2013 by Ulrik Torben Buchholtz
- License
- This work is licensed under a Creative Commons Attribution 3.0 Unported license (CC BY).
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