A. Beckmann:

"Dynamic ordinal analysis";

Archive for Mathematical Logic,42(2003), 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 $s\Pi^b_1$ 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

$s\Sigma^b_n(X)L^mIND$ for $m=n$ and $m=n+1$, $n\ge0$. 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.

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