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- Title
Enhancing induction in a contraction free logic with unrestricted abstraction: from Z to Z2.
- Authors
Petersen, Uwe
- Abstract
Z is a new type of non-finitist inference, i.e., an inference that involves treating some infinite collection as completed, designed for contraction free logic with unrestricted abstraction. It has been introduced in Petersen (Studia Logica 64:365–403, 2000) and shown to be consistent within a system L i D λ of contraction free logic with unrestricted abstraction. In Petersen (Arch Math Log 42(7):665–694, 2003) it was established that adding Z to L i D λ is sufficient to prove the totality of primitive recursive functions but it was also indicated that this would not extend to 2-recursive functions such as the Ackermann–Péter function, for instance. The purpose of the present paper is to expand the underlying idea in the construction of Z to gain a stronger notion, conveniently labeled Z 2 , which is sufficient to prove a form of nested double induction and thereby the totality of 2-recursive functions.
- Subjects
LOGIC; RECURSIVE functions
- Publication
Archive for Mathematical Logic, 2022, Vol 61, Issue 7/8, p1007
- ISSN
0933-5846
- Publication type
Article
- DOI
10.1007/s00153-022-00824-8