Epsilon substitution method for ID1(Π10∨Σ10)

Epsilon substitution method for elementary analysis

Epsilon Substitution for ID1

Hilbert’s epsilon substitution method provides a technique for showing that a theory is consistent by producing progressively more accurate computable approximations to the non-computable components of a proof. If it can be shown that this process eventually halts with a sufficiently good approximation, the theory is consistent. Here we produce a new formulation of the method for the theory ID1...

Epsilon substitution for transfinite induction

We apply Mints’ technique for proving the termination of the epsilon substitution method via cut-elimination to the system of Peano Arithmetic with Transfinite Induction given by Arai.

Epsilon–Substitution Method for the Ramified Language and ∆1-Comprehension Rule

We extend to Ramified Analysis the definition and termination proof of Hilbert’s substitution method. This forms a base for future extensions to predicatively reducible subsystems of analysis. First such system treated here is second order arithmetic with ∆1-comprehension rule. Introduction The epsilon substitution method is based on the language introduced by Hilbert [7]. The main non-boolean ...

Grigori Mints Thoralf Skolem and the Epsilon Substitution Method for Predicate Logic *

Skolem’s contributions to mathematical logic are fundamental and far-reaching. A good survey by Hao Wang (1970) is presented in Fenstad’s collection of Skolem’s works (1970). Even Skolemization, i.e. the replacement of quantifiers by new constant and function symbols, is too extensive for one talk. Cf. my survey (Mints 1990) of proof-theoretic aspects and more recent work (Shankar 1992) concern...