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Quasi-identity

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conditional identity

Formulas of a first-order logical language of the form

where and denote atomic formulas of the form

where are terms in and is a primitive predicate symbol. Quasi-varieties of algebraic systems are defined by quasi-identities (cf. Algebraic systems, quasi-variety of). An identity is a special case of a quasi-identity.


Comments

Quasi-identities are also commonly called Horn sentences.

References

[a1] A. Horn, "On sentences which are true of direct unions of algebras" J. Symbol. Logic , 16 (1951) pp. 14–21
[a2] P.M. Cohn, "Universal algebra" , Reidel (1981) pp. 235
How to Cite This Entry:
Quasi-identity. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Quasi-identity&oldid=39459
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article