arnold beckmann's pages
Dynamic ordinal analysis
Author: Arnold Beckmann
Title: Dynamic ordinal analysis
Journal: Archive for Mathematical Logic 2003, 42: 303-334
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
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
Different dynamic ordinals lead to separation.
Therefore, we will obtain several separation results between these
We will generalize our results to arbitrary languages extending the
language of Peano arithmetic.