Predicate symbol

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predicate letter

A notation for some concrete predicate or relation. E.g., the symbol often denotes the order relation on the real numbers; it is a -place predicate. In the formal structure of a language, the symbols denoting predicates must be used, in a well-defined way, for constructing expressions of the language. In particular, if is an -place predicate symbol, then the following rule should be among the syntactic rules for forming expressions in the formalized language: "If t1…tn are terms, then Pt1…tn is a formula" . Thus, predicate symbols are syntactically used to form formulas, and semantically denote predicates.

References

 [1] S.C. Kleene, "Introduction to metamathematics" , North-Holland (1951) [2] Yu.L. Ershov, E.A. Palyutin, "Mathematical logic" , Moscow (1970) (In Russian)

Comments

A predicate symbol is also called a relation symbol.

References

 [a1] Yu.I. Manin, "A course in mathematical logic" , Springer (1977) (Translated from Russian)
How to Cite This Entry:
Predicate symbol. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Predicate_symbol&oldid=16839
This article was adapted from an original article by V.N. Grishin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article