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$$S^ i_ 3$$ and $$\overset\circ V^ i_ 2(BD)$$. (English) Zbl 0681.03040
See the preview in Zbl 0665.03041.

##### MSC:
 03F30 First-order arithmetic and fragments 03F35 Second- and higher-order arithmetic and fragments 03F25 Relative consistency and interpretations 03D15 Complexity of computation (including implicit computational complexity)
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##### References:
 [1] Buss, S.: Bounded arithmetic. Napoli: Bibliopolis 1986 · Zbl 0649.03042 [2] Buss, S.: Axiomatizations and conservation results for fragments of bounded arithmetic. (To appear in: Contemporary Mathematics AMS, Proc. of Workshop in Logic and Computation, 1987) · Zbl 0699.03032 [3] Nelson, E.: Predicative arithmetic. Princeton University Press, 1986 · Zbl 0617.03002 [4] Wilkie, A., Paris, J.: On the scheme of induction for bounded arithmetic formulas. Ann. Pure Appl. Logic35, 267–302 (1987) · Zbl 0647.03046 · doi:10.1016/0168-0072(87)90066-2 [5] Takeuti, G.: Bounded arithmetic and truth definition. Ann. Pure Appl. Logic39, 75–104 (1988) · Zbl 0653.03038 · doi:10.1016/0168-0072(88)90046-2 [6] Takeuti, G.: Some relations among systems for bounded arithmetic. (To appear in: Petkov, P. (ed), Heyting: Mathematical logic. London, Plenum Press) · Zbl 0790.03057
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