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Dynamic ordinal analysis / Arnold Beckmann

Archive for Mathematical Logic, Volume: 42, Issue: 4, Pages: 303 - 334

Swansea University Author: Arnold, Beckmann

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Abstract

Dynamic ordinal analysis is ordinal analysis for weak arithmetics like fragments of bounded arithmetic. In this paper we will define dynamic ordinals - they will be sets of number theoretic functions measuring the amount of Π b 1 (α) order induction available in a theory. We will compare order induc...

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Published in: Archive for Mathematical Logic
ISSN: 0933-5846 1432-0665
Published: Springer 2002
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa1701
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Abstract: Dynamic ordinal analysis is ordinal analysis for weak arithmetics like fragments of bounded arithmetic. In this paper we will define dynamic ordinals - they will be sets of number theoretic functions measuring the amount of Π b 1 (α) order induction available in a theory. We will compare order induction to successor induction over weak theories. We will compute dynamic ordinals of the bounded arithmetic theories Σ b n (α)-LmIND for m=n and m=n+1, n≥0 . Different dynamic ordinals lead to separation. Therefore, we will obtain several separation results between these relativized theories. We will generalize our results to arbitrary languages extending the language of Peano arithmetic.
College: College of Science
Issue: 4
Start Page: 303
End Page: 334