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Details
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| Supervisor: |
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Prof. Stan
S. Wainer |
| E-mail address: |
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espoors
@ maths.leeds.ac.uk |
| Department: |
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Pure
Mathematics |
| Mathematical Interests: |
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Mathematical
Logic, Proof Theory, Philosophy of Mathematics.
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Contents
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Thesis:
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A
Hierarchy of Ramified Theories Below Primitve Recursive Artihmetic
(submitted
November 2008)
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Selected Talks: |
Elementary Arithmetic (.pdf)
BLC 2005,
Bristol, and MATHLOGAPS Workshop
2005, Fischbachau.
A
Hierarchy of Ramified Theories Below Primitve Recursive
Artihmetic (.pdf)
Leeds Logic
Seminar, 22nd October 2008.
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Research Outline:
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The theory EA(I;O), developed by Prof. S. Wainer and former research
students, aims to incorporate Simmons/Bellantoni-Cook stlye variable
separation into first order artihmetic. It replaces the usual induction
axiom schema of Peano Arithmetic with a two-sorted 'predicative'
induction rule.
The result
is a theory whose provably recursive functions are Grzegorczyk's E3.
The slow-growing proof theoretical ordinal of the theory may be seen as
epsilon-0. In my thesis I attempt to define a hierarchy of theories
based on EA(I;O) whose provably recursive functions correspond with
the Grzegorczyk hierarchy above E3.
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Personal Page (under
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