About: Morse–Kelley set theory

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Morse–Kelley set theory Goto Sponge NotDistinct Permalink

An Entity of Type : dbo:Work, within Data Space : el.dbpedia.org associated with source document(s)

In the foundations of mathematics, Morse–Kelley set theory (MK), Kelley–Morse set theory (KM), Morse–Tarski set theory (MT), Quine–Morse set theory (QM) or the system of Quine and Morse is a first-order axiomatic set theory that is closely related to von Neumann–Bernays–Gödel set theory (NBG). While von Neumann–Bernays–Gödel set theory restricts the bound variables in the schematic formula appearing in the axiom schema of Class Comprehension to range over sets alone, Morse–Kelley set theory allows these bound variables to range over proper classes as well as sets, as first suggested by Quine in 1940 for his system ML.

Attributes	Values
rdf:type	work
rdfs:label	Morse–Kelley set theory (en)
rdfs:comment	In the foundations of mathematics, Morse–Kelley set theory (MK), Kelley–Morse set theory (KM), Morse–Tarski set theory (MT), Quine–Morse set theory (QM) or the system of Quine and Morse is a first-order axiomatic set theory that is closely related to von Neumann–Bernays–Gödel set theory (NBG). While von Neumann–Bernays–Gödel set theory restricts the bound variables in the schematic formula appearing in the axiom schema of Class Comprehension to range over sets alone, Morse–Kelley set theory allows these bound variables to range over proper classes as well as sets, as first suggested by Quine in 1940 for his system ML. (en)
sameAs	Morse–Kelley set theory
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Cite_book dbt:Harvtxt dbt:Mathematical_logic dbt:Set_theory
Subject	Systems of set theory
gold:hypernym	Myth
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Morse–Kelley_set_theory?oldid=1043549828&ns=0
Wikipage page ID	2693655 (xsd:integer)
page length (characters) of wiki page	20753 (xsd:nonNegativeInteger)
Wikipage revision ID	1043549828 (xsd:integer)
Link from a Wikipage to another Wikipage	Foundations of mathematics Unary operation Union (set theory) Well-order Willard Van Orman Quine Algebra of sets Anthony Morse Atomic sentence Axiom of choice Axiom of empty set Axiom of extensionality Axiom of global choice Axiom of infinity Axiom of limitation of size Axiom of pairing Axiom of power set Axiom of regularity Axiom of union Axiom schema Axiom schema of replacement Axiom schema of specification Bijection Semantics Thoralf Skolem Universe (mathematics) Urelement Von Neumann universe Von Neumann–Bernays–Gödel set theory Cardinal number Cartesian product Free variables and bound variables David Lewis (philosopher) Disjoint sets Domain of a function Domain of discourse Jean E. Rubin Power set Second-order logic Set-builder notation Set (mathematics) Set theory Surjective function Zermelo–Fraenkel set theory Class (set theory) Predicate (mathematical logic) Conservative extension Constructible universe John L. Kelley John Lemmon Mostowski Ontology Order theory Ordered pair Ordinal number Empty set First-order logic Function (mathematics) Composition operator Impredicativity Inaccessible cardinal Mnemonic Syntax Infinite set Injective function Integer Peano axioms Transfinite induction Subset Topology Limit ordinal History of numbers New Foundations Range of a function Rational number Real number Relation (mathematics) Singleton (mathematics) Systems of set theory
has abstract	In the foundations of mathematics, Morse–Kelley set theory (MK), Kelley–Morse set theory (KM), Morse–Tarski set theory (MT), Quine–Morse set theory (QM) or the system of Quine and Morse is a first-order axiomatic set theory that is closely related to von Neumann–Bernays–Gödel set theory (NBG). While von Neumann–Bernays–Gödel set theory restricts the bound variables in the schematic formula appearing in the axiom schema of Class Comprehension to range over sets alone, Morse–Kelley set theory allows these bound variables to range over proper classes as well as sets, as first suggested by Quine in 1940 for his system ML. Morse–Kelley set theory is named after mathematicians John L. Kelley and Anthony Morse and was first set out by and later in an appendix to Kelley's textbook General Topology (1955), a graduate level introduction to topology. Kelley said the system in his book was a variant of the systems due to Thoralf Skolem and Morse. Morse's own version appeared later in his book A Theory of Sets (1965). While von Neumann–Bernays–Gödel set theory is a conservative extension of Zermelo–Fraenkel set theory (ZFC, the canonical set theory) in the sense that a statement in the language of ZFC is provable in NBG if and only if it is provable in ZFC, Morse–Kelley set theory is a proper extension of ZFC. Unlike von Neumann–Bernays–Gödel set theory, where the axiom schema of Class Comprehension can be replaced with finitely many of its instances, Morse–Kelley set theory cannot be finitely axiomatized. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Morse–Kelley_set_theory
is notableIdea of	Willard Van Orman Quine
is Wikipage redirect of	Morse--Kelley set theory Morse-Kelley set theory Morse-Kelly set theory Kelley-Morse set theory

Faceted Search & Find service v1.17_git151 as of Feb 20 2025

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 07.20.3240 as of Nov 11 2024, on Linux (x86_64-ubuntu_focal-linux-gnu), Single-Server Edition (72 GB total memory, 1 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2025 OpenLink Software