Systems of explicit mathematics with non-constructive μ-operator. Part I

Annals of Pure and Applied Logic 65 (3):243-263 (1993)

Abstract

Feferman, S. and G. Jäger, Systems of explicit mathematics with non-constructive μ-operator. Part I, Annals of Pure and Applied Logic 65 243-263. This paper is mainly concerned with the proof-theoretic analysis of systems of explicit mathematics with a non-constructive minimum operator. We start off from a basic theory BON of operators and numbers and add some principles of set and formula induction on the natural numbers as well as axioms for μ. The principal results then state: BON plus set induction is proof-theoretically equivalent to Peano arithmetic PA; BON plus formula induction is proof-theoretically equivalent to the system <0 of second-order arithmetic

Download options

PhilArchive



    Upload a copy of this work     Papers currently archived: 72,694

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Analytics

Added to PP
2014-01-16

Downloads
32 (#361,103)

6 months
1 (#388,319)

Historical graph of downloads
How can I increase my downloads?

References found in this work

A Well-Ordering Proof for Feferman's theoryT 0.Gerhard Jäger - 1983 - Archive for Mathematical Logic 23 (1):65-77.
Fixed Points in Peano Arithmetic with Ordinals.Gerhard Jäger - 1993 - Annals of Pure and Applied Logic 60 (2):119-132.

Add more references

Citations of this work

The Unfolding of Non-Finitist Arithmetic.Solomon Feferman & Thomas Strahm - 2000 - Annals of Pure and Applied Logic 104 (1-3):75-96.
On Feferman’s Operational Set Theory OST.Gerhard Jäger - 2007 - Annals of Pure and Applied Logic 150 (1-3):19-39.
Totality in Applicative Theories.Gerhard Jäger & Thomas Strahm - 1995 - Annals of Pure and Applied Logic 74 (2):105-120.

View all 20 citations / Add more citations

Similar books and articles

Can Constructive Mathematics Be Applied in Physics?Douglas S. Bridges - 1999 - Journal of Philosophical Logic 28 (5):439-453.
Power Types in Explicit Mathematics?Gerhard Jäger - 1997 - Journal of Symbolic Logic 62 (4):1142-1146.
Realisability in Weak Systems of Explicit Mathematics.Daria Spescha & Thomas Strahm - 2011 - Mathematical Logic Quarterly 57 (6):551-565.
Explicit Mathematics with the Monotone Fixed Point Principle.Michael Rathjen - 1998 - Journal of Symbolic Logic 63 (2):509-542.