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

Annals of Pure and Applied Logic 79 (1):37-52 (1996)


This paper is mainly concerned with proof-theoretic analysis of some second-order systems of explicit mathematics with a non-constructive minimum operator. By introducing axioms for variable types we extend our first-order theory BON to the elementary explicit type theory EET and add several forms of induction as well as axioms for μ. The principal results then state: EET plus set induction is proof-theoretically equivalent to Peano arithmetic PA <0)

Download options


    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


Added to PP

33 (#350,156)

6 months
1 (#388,319)

Historical graph of downloads
How can I increase my downloads?

References found in this work

Totality in Applicative Theories.Gerhard Jäger & Thomas Strahm - 1995 - Annals of Pure and Applied Logic 74 (2):105-120.

Add more references

Citations of this work

Hilbert’s Program.Richard Zach - 2003 - In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab, Center for the Study of Language and Information, Stanford University.
Why a Little Bit Goes a Long Way: Logical Foundations of Scientifically Applicable Mathematics.Solomon Feferman - 1992 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:442 - 455.
The Unfolding of Non-Finitist Arithmetic.Solomon Feferman & Thomas Strahm - 2000 - Annals of Pure and Applied Logic 104 (1-3):75-96.

View all 24 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.