Abstract
Hilbert proposed the epsilon substitution method as a basis for consistency proofs. Hilbert's Ansatz for finding a solving substitution for any given finite set of transfinite axioms is, starting with the null substitution S 0, to correct false values step by step and thereby generate the process S 0,S 1,… . The problem is to show that the approximating process terminates. After Gentzen's innovation, Ackermann (Maths. Ann. 117 (1940) 162) succeeded to prove termination of the process for first order arithmetic. Inspired by G. Mints (draft June 1, 2000) as an Ariadne's thread we formulate the epsilon substitution method for the theory ID 1(Π 1 0 ∨ Σ 1 0) of non-iterated inductive definitions for disjunctions of simply universal and existential operators, and give a termination proof of the H-process based on Ackermann (Maths. Ann. 117 (1940) 162). The termination proof is based on transfinite induction up to the Howard ordinal.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
