| 单词 | proof theory |
| 释义 | > as lemmasproof theory proof theory n. Mathematics the branch of mathematics concerned with the syntactic (as opposed to semantic) properties of formulae and proofs in formal systems. ΘΚΠ the world > relative properties > number > mathematics > [noun] > theories or branches of menadry1570 pure mathematics1605 mechanics1612 residuation1846 chaos theory1880 number theory1901 formalism1913 intuitionism1913 replacement theory1914 biomathematics1923 proof theory1929 finitism1935 mereology1938 combinatorics1941 cryptarithmetic1943 game theory1945 numerical analysis1946 queueing theory1951 constructivism1959 complexity1963 catastrophe theory1971 chaology1985 the mind > mental capacity > philosophy > mathematical philosophy > [noun] > doctrines of number theory1899 mathematicism1917 proof theory1929 finitism1935 constructivism1959 1929 H. Weyl in Rice Inst. Pamphlet 16 146 The intention of the Hilbert proof theory is to atone..for the continual titanic offenses which mathematics and all mathematicians have committed and will still commit against mind. 1969 Listener 10 July 44/2 The analogy he was using was one with proof theory in logic, where from initial axioms and rules of inference you can produce true theorems—rather like doing geometry exercises in school. 2004 M. Potter Set Theory & its Philos. xi. 189 Of special interest to logicians has been the discovery that transfinite induction can be used in harness with cut elimination in proof theory to demonstrate the consistency of various formal systems. < as lemmas |
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