Axiomatizations and conservation results for fragments of bounded arithmetic
Samuel R. Buss · Contemporary mathematics - American Mathematical Society · 1990
This paper presents new results on axiomatizations for fragments of Bounded Arithmetic which improve upon the author’s dissertation. It is shown that (Σb i+1 ∩ Πbi+1)-PIND and strong Σbi-replacement are consequences of Si 2. Also ∆bi+1-IND is a consequence of T i 2. The latter result is proved by showing that S i+1 2 is ∀∃Σb i+1-conservative over is conservative over T i 2 +Σbi+1-replacement T i 2. Furthermore, Si+1 2 with respect to Boolean combinations of Σb i+1-formulas. 1