Journal of Symbolic Logic

Proper Classes via the Iterative Conception of Set

Mark F. Sharlow

Full-text is available via JSTOR, for JSTOR subscribers. Go to this article in JSTOR.

Abstract

We describe a first-order theory of generalized sets intended to allow a similar treatment of sets and proper classes. The theory is motivated by the iterative conception of set. It has a ternary membership symbol interpreted as membership relative to a set-building step. Set and proper class are defined notions. We prove that sets and proper classes with a defined membership form an inner model of Bernays-Morse class theory. We extend ordinal and cardinal notions to generalized sets and prove ordinal and cardinal results in the theory. We prove that the theory is consistent relative to $\mathrm{ZFC} + (\exists x) \lbrack x \text{is a strongly inaccessible cardinal}\rbrack$.

Article information

Source
J. Symbolic Logic, Volume 52, Issue 3 (1987), 636-650.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183742432

Mathematical Reviews number (MathSciNet)
MR902980

Zentralblatt MATH identifier
0646.03044

JSTOR
links.jstor.org

Citation

Sharlow, Mark F. Proper Classes via the Iterative Conception of Set. J. Symbolic Logic 52 (1987), no. 3, 636--650. https://projecteuclid.org/euclid.jsl/1183742432


Export citation