Vol. 72, No. 2, 1977

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An Ehrenfeucht game for the multivariable quantifiers of Malitz and some applications

Lee Wilson Badger

Vol. 72 (1977), No. 2, 293–304
Abstract

An Ehrenfeucht game is developed for some languages which admit the Malitz quantifiers. The method is used to show that equivalence of structures with respect to such languages is usually preserved by the cardinal sum operation, and that such equivalence need not be preserved by the direct product operation. Craig’s theorem is shown to fail in all cardinal interpretations of the languages.

Mathematical Subject Classification
Primary: 02B20, 02B20
Secondary: 02H05
Milestones
Received: 27 October 1976
Revised: 26 April 1977
Published: 1 October 1977
Authors
Lee Wilson Badger