Horn sentences in identity theory
Keyword(s):
Horn [2] obtained a sufficient condition for an elementary class to be closed under direct product. Chang and Morel [1] showed that this is not a necessary condition. We will show that, if consideration is restricted to identity theory, that is, a first-order predicate calculus with equality but no other relation symbols or operation symbols, Horn's condition is necessary and sufficient.A model for identity theory consists of a non-empty domain A, but no relations or operations except equality. If I is an index set, and for each is a model for identity theory, then the direct product of the is a model for identity theory and has domain A, the cartesian product of the Ai.
1990 ◽
Vol 32
(2)
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pp. 180-192
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2021 ◽
Vol 2
(2)
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pp. 30-37
2012 ◽
Vol 22
(06)
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pp. 1250052
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2019 ◽
Vol 33
(10)
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pp. 1950086
2020 ◽
Vol 100
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pp. 106040
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