Epsilon Substitution for 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.

Cut elimination for a simple formulation of epsilon calculus

A simple cut elimination proof for arithmetic with epsilon symbol is used to establish termination of a modified epsilon substitution process. This opens a possibility of extension to much stronger systems.

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 ...

ON ($epsilon, epsilon vee q$)-FUZZY IDEALS OF BCI-ALGEBRAS

The aim of this paper is to introduce the notions of ($epsilon, epsilon vee q$)-fuzzy p-ideals, ($epsilon, epsilon vee q$)-fuzzy q-ideals and ($epsilon, epsilon vee q$)-fuzzy a-ideals in BCIalgebras and to investigate some of their properties. Several characterizationtheorems for these generalized fuzzy ideals are proved and the relationshipamong these generalized fuzzy ideals of BCI-algebras i...

Epsilon substitution method for elementary analysis