Journal article 1186 views
Dynamic ordinal analysis
Archive for Mathematical Logic, Volume: 42, Issue: 4, Pages: 303 - 334
Swansea University Author:
Arnold Beckmann
Full text not available from this repository: check for access using links below.
DOI (Published version): 10.1007/s00153-002-0169-4
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...
| 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 |
| 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: |
Faculty of Science and Engineering |
| Issue: |
4 |
| Start Page: |
303 |
| End Page: |
334 |