Some theories with positive induction of ordinal strength φω0

Jäger, Gerhard; Strahm, Thomas (1996). Some theories with positive induction of ordinal strength φω0. The journal of symbolic logic, 61(3), pp. 818-842. Cambridge University Press 10.2307/2275787

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This paper deals with: (i) the theory ID*# which results ÎD1 from by restricting induction on the natural numbers to formulas which are positive in the fixed point constants, (ii) the theory BON(μ) plus various forms of positive induction, and (iii) a subtheory of Peano arithmetic with ordinals in which induction on the natural numbers is restricted to formulas which are Σ in the ordinals. We show that these systems have proof-theoretic strength φω0.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Institute of Computer Science (INF)

UniBE Contributor:

Jäger, Gerhard Max and Strahm, Thomas Adrian

Subjects:

000 Computer science, knowledge & systems
500 Science > 510 Mathematics

ISSN:

0022-4812

Publisher:

Cambridge University Press

Language:

English

Submitter:

Marceline Brodmann

Date Deposited:

28 Jul 2020 11:52

Last Modified:

28 Jul 2020 11:52

Publisher DOI:

10.2307/2275787

BORIS DOI:

10.7892/boris.115713

URI:

https://boris.unibe.ch/id/eprint/115713

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