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Morse–Kelley set theory

Definition

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.

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L. Kelley Jean E. Rubin John L. 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Quine W. V. O. Quine W. V. Quine Well-formed formula Well-order Willard Van Orman Quine ZFC Zermelo set theory Zermelo–Fraenkel set theory

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