On Use of an Explicit Congruence Predicate in Bounded Arithmetic

Details On Use of an Explicit Congruence Predicate in Bounded Arithmetic On Use of an Explicit Congruence Predicate in Bounded Arithmetic

2009-04-02

arxiv.org/abs/0904.0335v1

Mathematics

Logic

17 Pages

Scientific paper

We introduce system S^2_0E, a bounded arithmetic corresponding to Buss's
S^2_0 with the predicate E which signifies the existence of the value. Then, we
show that we can \Sigma^b_2-define truthness of S^2_0 E and therefore we can
prove consistency of S^2_0 E in S^2_2. Finally, we conjecture that S^2_0 E +
\Sigma^b_1-PIND interprets S^2_1.

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