Proper classes via the iterative conception of set

Journal of Symbolic Logic 52 (3):636-650 (1987)
  Copy   BIBTEX

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 ZFC + (∃ x) [ x is a strongly inaccessible cardinal]

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 94,659

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

On the iterative explanation of the paradoxes.Christopher Menzel - 1986 - Philosophical Studies 49 (1):37 - 61.
Wide Sets, ZFCU, and the Iterative Conception.Christopher Menzel - 2014 - Journal of Philosophy 111 (2):57-83.
Mereological sets of distributive classes.Andrzej Pietruszczak - 1996 - Logic and Logical Philosophy 4:105-122.
Classless.Sam Roberts - 2020 - Analysis 80 (1):76-83.
Finiteness Classes and Small Violations of Choice.Horst Herrlich, Paul Howard & Eleftherios Tachtsis - 2016 - Notre Dame Journal of Formal Logic 57 (3):375-388.
A set theory with Frege-Russell cardinal numbers.Alan McMichael - 1982 - Philosophical Studies 42 (2):141 - 149.
Labelling classes by sets.M. Victoria Marshall & M. Gloria Schwarze - 2005 - Archive for Mathematical Logic 44 (2):219-226.

Analytics

Added to PP
2009-01-28

Downloads
66 (#243,357)

6 months
7 (#624,553)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Citations of this work

Broadening the Iterative Conception of Set.Mark F. Sharlow - 2001 - Notre Dame Journal of Formal Logic 42 (3):149-170.
The intuitionistic alternative set theory.K. Lano - 1993 - Annals of Pure and Applied Logic 59 (2):141-156.

Add more citations

References found in this work

Mathematics in Philosophy, Selected Essays.Stewart Shapiro - 1983 - Journal of Symbolic Logic 53 (1):320.

Add more references