Finite Sets and Natural Numbers in Intuitionistic TT

Notre Dame Journal of Formal Logic 37 (4):585-601 (1996)
  Copy   BIBTEX

Abstract

We show how to interpret Heyting's arithmetic in an intuitionistic version of TT, Russell's Simple Theory of Types. We also exhibit properties of finite sets in this theory and compare them with the corresponding properties in classical TT. Finally, we prove that arithmetic can be interpreted in intuitionistic TT, the subsystem of intuitionistic TT involving only three types. The definitions of intuitionistic TT and its finite sets and natural numbers are obtained in a straightforward way from the classical definitions. This is very natural and seems to make intuitionistic TT an interesting intuitionistic set theory to study, beside intuitionistic ZF

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,323

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

Models of intuitionistic TT and N.Daniel Dzierzgowski - 1995 - Journal of Symbolic Logic 60 (2):640-653.
On Infinite Number and Distance.Jeremy Gwiazda - 2012 - Constructivist Foundations 7 (2):126-130.
The ordertype of β-r.E. Sets.Klaus Sutner - 1990 - Journal of Symbolic Logic 55 (2):573-576.
Numbers and Everything.Gonçalo Santos - 2013 - Philosophia Mathematica 21 (3):297-308.
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.
Impure Sets Are Not Located: A Fregean Argument.Roy T. Cook - 2012 - Thought: A Journal of Philosophy 1 (3):219-229.

Analytics

Added to PP
2010-08-24

Downloads
16 (#911,799)

6 months
5 (#648,315)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

New Foundations for Mathematical Logic.W. V. Quine - 1937 - Journal of Symbolic Logic 2 (2):86-87.
A set of axioms for logic.Theodore Hailperin - 1944 - Journal of Symbolic Logic 9 (1):1-19.
Models of intuitionistic TT and N.Daniel Dzierzgowski - 1995 - Journal of Symbolic Logic 60 (2):640-653.
Arithmetic and the theory of types.M. Boffa - 1984 - Journal of Symbolic Logic 49 (2):621-624.

Add more references