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The omega-rule interpretation of transfinite provability logic.
- Source :
-
Annals of Pure & Applied Logic . Apr2018, Vol. 169 Issue 4, p333-371. 39p. - Publication Year :
- 2018
-
Abstract
- Given a computable ordinal Λ, the transfinite provability logic GLP Λ has for each ξ < Λ a modality [ ξ ] intended to represent a provability predicate within a chain of increasing strength. One possibility is to read [ ξ ] ϕ as ϕ is provable in T using ω-rules of depth at most ξ, where T is a second-order theory extending ACA 0 . In this paper we will formalize such iterations of ω -rules in second-order arithmetic and show how it is a special case of what we call uniform provability predicates. Uniform provability predicates are similar to Ignatiev's strong provability predicates except that they can be iterated transfinitely. Finally, we show that GLP Λ is sound and complete for any uniform provability predicate. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01680072
- Volume :
- 169
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Annals of Pure & Applied Logic
- Publication Type :
- Academic Journal
- Accession number :
- 127790494
- Full Text :
- https://doi.org/10.1016/j.apal.2017.12.006