Frege's theorem in a constructive setting

Journal of Symbolic Logic 64 (2):486-488 (1999)
  Copy   BIBTEX


then E has a subset which is the domain of a model of Peano's axioms for the natural numbers. (This result is proved explicitly, using classical reasoning, in section 3 of [1].) My purpose in this note is to strengthen this result in two directions: first, the premise will be weakened so as to require only that the map ν be defined on the family of (Kuratowski) finite subsets of the set E, and secondly, the argument will be constructive, i.e., will involve no use of the law of excluded middle. To be precise, we will prove, in constructive (or intuitionistic) set theory3, the following..



    Upload a copy of this work     Papers currently archived: 83,836

External links

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

Through your library

Similar books and articles

Developments in constructive nonstandard analysis.Erik Palmgren - 1998 - Bulletin of Symbolic Logic 4 (3):233-272.
A Constructive View on Ergodic Theorems.Bas Spitters - 2006 - Journal of Symbolic Logic 71 (2):611 - 623.
Boolean Algebras and Distributive Lattices Treated Constructively.John L. Bell - 1999 - Mathematical Logic Quarterly 45 (1):135-143.
Toward a constructive theory of unbounded linear operators.Feng Ye - 2000 - Journal of Symbolic Logic 65 (1):357-370.
On the Strength of some Semi-Constructive Theories.Solomon Feferman - 2012 - In Ulrich Berger, Hannes Diener, Peter Schuster & Monika Seisenberger (eds.), Logic, Construction, Computation. De Gruyter. pp. 201-226.
On the constructive Dedekind reals.Robert S. Lubarsky & Michael Rathjen - 2008 - Logic and Analysis 1 (2):131-152.


Added to PP

245 (#60,464)

6 months
1 (#497,632)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

John L. Bell
University of Western Ontario

Citations of this work

Speaking with Shadows: A Study of Neo‐Logicism.Fraser MacBride - 2003 - British Journal for the Philosophy of Science 54 (1):103-163.
Frege meets Brouwer.Stewart Shapiro & Øystein Linnebo - 2015 - Review of Symbolic Logic 8 (3):540-552.
The Potential in Frege’s Theorem.Will Stafford - 2023 - Review of Symbolic Logic 16 (2):553-577.
Finite sets and Frege structures.John L. Bell - 1999 - Journal of Symbolic Logic 64 (4):1552-1556.

Add more citations