@inbook{10.2307/j.ctt7ztgtr.26,
URL = {http://www.jstor.org/stable/j.ctt7ztgtr.26},
abstract = {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},
bookauthor = {Edward Nelson},
booktitle = {Predicative Arithmetic. (MN-32):},
pages = {111--114},
publisher = {Princeton University Press},
title = {Proofs},
year = {1986}
}