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finitary
In mathematics or logic, a finitary operation is an operation that takes a finite number of input values to produce an output, like those of arithmetic. Operations on infinite numbers of input values are called ''infinitary''.
==Finitary argument==
A finitary argument is one which can be translated into a finite set of symbolic propositions starting from a finite〔The number of axioms ''referenced'' in the argument will necessarily be finite since the proof is finite, but the number of axioms from which these are ''chosen'' is infinite when the system has axiom schemes, as for example the axiom schemes of propositional calculus.〕 set of axioms. In other words, it is a proof (including all assumptions) that can be written on a large enough sheet of paper.
By contrast, infinitary logic studies logics that allow infinitely long statements and proofs. In such a logic, one can regard the existential quantifier, for instance, as derived from an infinitary disjunction.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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