Predicate symbol
From Encyclopedia of Mathematics
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
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
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