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Metamathematics is the study of mathematics itself using mathematical methods. This study produces metatheories , which are mathematical theories about other mathematical theories. Emphasis on metamathematics (and perhaps the creation of the term itself) owes itself to David Hilbert 's attempt to secure the foundations of mathematics in the ...
Stephen Cole Kleene (/ ˈ k l eɪ n i / KLAY-nee; [a] January 5, 1909 – January 25, 1994) was an American mathematician.One of the students of Alonzo Church, Kleene, along with Rózsa Péter, Alan Turing, Emil Post, and others, is best known as a founder of the branch of mathematical logic known as recursion theory, which subsequently helped to provide the foundations of theoretical computer ...
The metamathematics of Zermelo–Fraenkel set theory has been extensively studied. Landmark results in this area established the logical independence of the axiom of choice from the remaining Zermelo-Fraenkel axioms and of the continuum hypothesis from ZFC.
Created Date: 8/30/2012 4:52:52 PM
In logic, Richard's paradox is a semantical antinomy of set theory and natural language first described by the French mathematician Jules Richard in 1905. The paradox is ordinarily used to motivate the importance of distinguishing carefully between mathematics and metamathematics.
The metamathematics of algebraic systems, collected papers:1936-1967 by A.I. Malcev, Amsterdam, North-Holland Pub. Co., 1971, ISBN 0-7204-2266-3 (xvii+494 p.; trans., ed. and provided with additional notes by Benjamin Franklin Wells, III) Algorithms and recursive functions by A. I. Malcev, Groningen, Wolters-Noordhoff Pub. Co. 1970 [7]
Metamath is a formal language and an associated computer program (a proof assistant) for archiving and verifying mathematical proofs. [2] Several databases of proved theorems have been developed using Metamath covering standard results in logic, set theory, number theory, algebra, topology and analysis, among others.
Gregory John Chaitin (/ ˈ tʃ aɪ t ɪ n / CHY-tin; born 25 June 1947) is an Argentine-American mathematician and computer scientist.Beginning in the late 1960s, Chaitin made contributions to algorithmic information theory and metamathematics, in particular a computer-theoretic result equivalent to Gödel's incompleteness theorem. [2]