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Predicate variable

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second-order variable

A variable whose values can be predicates (cf. Predicate). In the formal structure of an axiomatic system, predicate variables differ from individual variables (cf. Individual variable) by the fact that formulas may be substituted for them. Thus, in second-order predicate calculus, if in the axiom

is a predicate variable for -place predicates, then any formula with distinguished variables may be taken for . Here the result of substituting a formula with distinguished variables for the predicate variable in the atomic formula , where are individual constants, is the formula obtained from by simultaneously replacing the free occurrences of by , respectively.

References

[1] A. Church, "Introduction to mathematical logic" , 1 , Princeton Univ. Press (1956)
[2] G. Takeuti, "Proof theory" , North-Holland (1987)
How to Cite This Entry:
Predicate variable. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Predicate_variable&oldid=48278
This article was adapted from an original article by V.N. Grishin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article