Predicate variable
From Encyclopedia of Mathematics
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=15757
Predicate variable. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Predicate_variable&oldid=15757
This article was adapted from an original article by V.N. Grishin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article