TL;DRAbstract
Bounded arithmetic was proposed in Parikh (1971), in connection with length-ofproofs questions. He called his system PB, presumably as the alphabetical successor to PA, but we shall stay with the established name I Δ0 (for “induction for Δ0 formulas”). This theory and its extensions by axioms saying that some particular recursive function is total were studied and developed in the fundamental work of J. Paris and A. Wilkie, and their students C. Dimitracopoulos, R. Kaye, and A. Woods.
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Bounded arithmetic was proposed in Parikh (1971), in connection with length-ofproofs questions. He called his system PB, presumably as the alphabetical successor to PA, but we shall stay with the established name I Δ0 (for “induction for Δ0 formulas”). This theory and its extensions by axioms saying that some particular recursive function is total were studied and developed in the fundamental work of J. Paris and A. Wilkie, and their students C. Dimitracopoulos, R. Kaye, and A. Woods.
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