Arithmetic without the successor axiom

Abstract

Second-order Peano Arithmetic minus the Successor Axiom is developed from first principles through Quadratic Reciprocity and a proof of self-consistency. This paper combines 4 other papers of the author in a self-contained exposition

Categories

Keywords

Reprint years

Links

PhilArchive

External links

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

Through your library

  • Only published works are available at libraries.

My notes

Similar books and articles

Proving quadratic reciprocity.Andrew Boucher - manuscript
"True" arithmetic can prove its own consistency.Andrew Boucher -
Equivalence of F with a sub-theory of peano arithmetic.Andrew Boucher - manuscript
Sub-Theory of Peano Arithmetic.Andrew Boucher - unknown
Proving Bertrand's postulate.Andrew Boucher - manuscript
Predicative fragments of Frege arithmetic.Øystein Linnebo - 2004 - Bulletin of Symbolic Logic 10 (2):153-174.
General arithmetic.Andrew Boucher - manuscript
Quadratic forms in models of IΔ0+ Ω1. I.Paola D’Aquino & Angus Macintyre - 2007 - Annals of Pure and Applied Logic 148 (1):31-48.
Systems for a foundation of arithmetic.Andrew Boucher - manuscript
Provable equality in primitive recursive arithmetic with and without induction.Harvey Friedman - 1975 - Pacific Journal of Mathematics 57 (2):379-392.

Analytics

Added to PP
2009-01-28

Downloads
150 (#129,740)

6 months
268 (#9,004)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Citations of this work

Add more citations

References found in this work

Logic, Logic, and Logic.George Boolos - 1998 - Cambridge, Mass: Harvard University Press. Edited by Richard C. Jeffrey.
Fixing Frege.John P. Burgess - 2005 - Princeton University Press.
Understanding the infinite.Shaughan Lavine - 1994 - Cambridge: Harvard University Press.
Frege's theory of numbers.Charles Parsons - 1964 - In Max Black (ed.), Philosophy in America. Ithaca: Routledge. pp. 180-203.
Existence and feasibility in arithmetic.Rohit Parikh - 1971 - Journal of Symbolic Logic 36 (3):494-508.

View all 14 references / Add more references