Vol. 27, No. 1, 1968

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Closed systems of functions and predicates

David Scott Geiger

Vol. 27 (1968), No. 1, 95–100

In this paper we show that there is a one to one correspondence between systems of functions defined on a finite set A and systems of predicates defined on A. This result implies that a complete set of invariants for a universal algebra on A is given by predicates defined on A. Conversely functions on A provide a complete system of invariants for sets of predicates closed under conjunction, change of variable and application of the existential quantifier.

Mathematical Subject Classification
Primary: 08.30
Received: 28 September 1967
Published: 1 October 1968
David Scott Geiger