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Minimal functional calculus

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minimal predicate calculus

The calculus of predicates given by all axiom schemes of the minimal propositional calculus and by the usual quantifier axiom schemes and deduction rules, that is,

$$\forall xA(x)\supset A(t),\quad A(t)\supset\exists xA(x)$$

($t$ an arbitrary term), modus ponens and

$$\frac{C\supset A(a)}{C\supset\forall xA(x)},\quad\frac{A(a)\supset C}{\exists xA(x)\supset C}$$

(provided the variable $a$ does not occur in $A(x)$ and $C$).

References

[1] A. Church, "Introduction to mathematical logic" , 1 , Princeton Univ. Press (1956)
How to Cite This Entry:
Minimal functional calculus. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Minimal_functional_calculus&oldid=12860
This article was adapted from an original article by S.K. Sobolev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article