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Axiomatizations and conservation results for fragments of bounded arithmetic. (English) Zbl 0699.03032
Logic and computation, Proc. Workshop, Pittsburgh/PA (USA) 1987, Contemp. Math. 106, 57-84 (1990).
[For the entire collection see Zbl 0691.00003.]
The paper is devoted to the problem of axiomatization of fragments of Bounded Arithmetic. It contains results which improve upon the author’s dissertation. It is shown that: 1) \((\Sigma^ b_{i+1}\cap \Pi^ b_{i+1})\)-PIND and strong \(\Sigma^ b_ i\)-replacement are consequences of \(S^ i_ 2\), 2) \(\Delta^ b_{i+1}\)-IND is a consequence of \(T^ i_ 2\), 3) \(S_ 2^{i+1}\) is \(\forall \exists \Sigma^ b_{i+1}\)-conservative over \(T^ i_ 2\), 4) \(S_ 2^{i+1}\) is conservative over \(T^ i_ 2+\Sigma^ b_{i+1}\)-replacement with respect to Boolean combinations of \(\Sigma^ b_{i+1}\)-formulas.
Reviewer: R.Murawski

MSC:
03F30 First-order arithmetic and fragments