Bulletin of Symbolic Logic

Reconsidering ordered pairs

Dominic McCarty and Dana Scott

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

The well known Wiener—Kuratowski explicit definition of the ordered pair, which sets 〈 x, y〉 = { {x } , {x, y } }, works well in many set theories but fails for those with classes which cannot be members of singletons. With the aid of the Axiom of Foundation, we propose a recursive definition of ordered pair which addresses this shortcoming and also naturally generalizes to ordered tuples of greater length. There are many advantages to the new definition, for it allows for uniform definitions working equally well in a wide range of models for set theories. In ZFC and closely related theories, the rank of an ordered pair of two infinite sets under the new definition turns out to be equal to the maximum of the ranks of the sets.

Article information

Source
Bull. Symbolic Logic Volume 14, Issue 3 (2008), 379-397.

Dates
First available in Project Euclid: 4 January 2009

Permanent link to this document
http://projecteuclid.org/euclid.bsl/1231081372

Digital Object Identifier
doi:10.2178/bsl/1231081372

Mathematical Reviews number (MathSciNet)
MR2440598

Zentralblatt MATH identifier
05532700

Citation

McCarty, Dominic; Scott, Dana. Reconsidering ordered pairs. Bulletin of Symbolic Logic 14 (2008), no. 3, 379--397. doi:10.2178/bsl/1231081372. http://projecteuclid.org/euclid.bsl/1231081372.


Export citation