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**Finitary**— In mathematics or logic, a finitary operation is one, like those of arithmetic, that takes a finite number of input values to produce an output. An operation such as taking an integral of a function, in calculus, is defined in such a way as to… … Wikipedia**Hilbert's program**— Hilbert s program, formulated by German mathematician David Hilbert in the 1920s, was to formalize all existing theories to a finite, complete set of axioms, and provide a proof that these axioms were consistent.Hilbert proposed that the… … Wikipedia**Brouwer-Hilbert controversy**— A foundational controversy in twentieth century history of mathematics opposed L. E. J. Brouwer, a supporter of intuitionism, and David Hilbert, the founder of formalism.BackgroundThe background for the controversy was set with David Hilbert s… … Wikipedia**set theory**— the branch of mathematics that deals with relations between sets. [1940 45] * * * Branch of mathematics that deals with the properties of sets. It is most valuable as applied to other areas of mathematics, which borrow from and adapt its… … Universalium**Metamathematics**— is the study of mathematics itself using mathematical methods. This study produces metatheories, which are mathematical theories about other mathematical theories. Metamathematical metatheorems about mathematics itself were originally… … Wikipedia**Pra**— may refer to:*Pra River *Physical Review A, a scientific journal, publication of the American Physical Society *Political Research Associates a nonprofit research group *Primitive recursive arithmetic, one proposed formalization of finitary… … Wikipedia**finitism**— In the philosophy of mathematics, the view that the only legitimate numbers are finite: ‘God created the integers, the rest is the work of man’ (L. Kronecker). In mathematics the restriction to finitary methods was advocated by David Hilbert. It… … Philosophy dictionary**transfinite induction**— The proof schema corresponding to ordinary mathematical induction taken into the transfinite, i.e. defined over orderings that may be larger than the standard ordering of the set of all natural numbers. Gentzen showed that if this operation is… … Philosophy dictionary**Mathematical logic**— (also known as symbolic logic) is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic.[1] The field includes both the mathematical study of logic and the… … Wikipedia**Philosophy of mathematics**— The philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of … Wikipedia