Adjective
(mathematics) Of a function, taking a finite number of arguments to produce an output.
(logic) Pertaining to finite-length proofs, each using a finite set of axioms.
Source: en.wiktionary.orgBut van Heijenoort says Herbrand's conception was "on the whole much closer to that of Hilbert's word 'finitary' ('finit') that to "intuitionistic" as applied to Brouwer's doctrine". Source: Internet
Hilbert was initially a deductivist, but, as may be clear from above, he considered certain metamathematical methods to yield intrinsically meaningful results and was a realist with respect to the finitary arithmetic. Source: Internet
He interpreted it as a kind of logical paradox, while in fact is just the opposite, namely a mathematical theorem within an absolutely uncontroversial part of mathematics (finitary number theory or combinatorics)." Source: Internet
Branches of model theory This article focuses on finitary first order model theory of infinite structures. Source: Internet
Hilbert accepted this proof as "finitary" although (as Gödel's theorem had already shown) it cannot be formalized within the system of arithmetic that is being proved consistent. Source: Internet
It should not be confused with relational algebra which deals in finitary relations (and in practice also finite and many-sorted). Source: Internet