### arnold beckmann's pages

## Dynamic ordinal analysis

**File:** PDF-File

**Author:** Arnold Beckmann

**Title:** Dynamic ordinal analysis

**Journal:** Archive for Mathematical Logic 2003, **42**: 303-334

**DOI:** 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 induction to successor induction over weak theories.
We will compute dynamic ordinals of the bounded arithmetic theories
Σ
b
n
(α)-L^{m}IND
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.