Definition of metamathematics in English:

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Pronunciation: /ˌmɛtəmaθ(ə)ˈmatɪks/

plural noun

[treated as singular]
The field of study that deals with the structure and formal properties of mathematics and similar formal systems.
Example sentences
  • Tarski made important contributions in many areas of mathematics: set theory, measure theory, topology, geometry, classical and universal algebra, algebraic logic, various branches of formal logic and metamathematics.
  • Proof theory, a form of metamathematics, studies the ways in which proofs are used in mathematics.
  • Thus, only in his early sixties did Hilbert truly proceed to create proof theory and metamathematics.



Example sentences
  • Gentzen's proof of the consistency of arithmetic is undoubtedly a very interesting metamathematical result, which may prove very stimulating and fruitful.
  • Meaning is then introduced at the metamathematical level, in the metalanguage.
  • Robinson's theory is based on the metamathematical fact that the system of real numbers is incomplete.




Example sentences
  • Perhaps some young metamathematician of the next generation will prove why this has to be so.
  • It is not easy to speculate just how a metamathematician should conduct himself in the pursuit of this discipline.
  • The study of formal calculi is more a job for metamathematicians than mathematicians.
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