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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