Provider: JSTOR http://www.jstor.org Database: JSTOR Content: text/plain; charset="us-ascii" TY - CHAP TI - Proofs A2 - Nelson, Edward AB -

We give a predicative arithmetization of the predicate calculus. We modify the treatment in [Sh, §2.6] by adopting tautological consequence as a rule of inference; see the conclusion of [Sh,§3.1].

24.1Def. Bis a substitution$axiom \leftrightarrow \exists \wedge \exists x\exists a$(ais substitutable forxin A &$B = {A_x}[a]\tilde \to \tilde \exists xA)$.

24.2Def. Bis an identity$axiom \leftrightarrow \exists x$(xis a variable &$B = x\tilde = x$.

24.3Def.Equals(x', y') = {(i, x'(z')"= y'(i)): i E Domx'}.

24.4Def. Equals(x', y') = {(i, x'(z')"= y'(i)): i E Domx'}.

24.5Def. B. is a logical$axiom \leftrightarrow \exists x$Def. Bis an equality axiom +-4 3x' 3y'(x' and y' are sequences of

EP - 114 PB - Princeton University Press PY - 1986 SN - null SP - 111 T2 - Predicative Arithmetic. (MN-32): UR - http://www.jstor.org/stable/j.ctt7ztgtr.26 Y2 - 2021/06/15/ ER -