metamathematics造句

• The discovery of hyperbolic geometry had important philosophical consequences for Metamathematics.
• David Hilbert founded metamathematics as a discipline for discussing formal systems.
• He objected to restricting the role of metamathematics to the foundations of mathematics.
• The previous section says more about the relevant metamathematics.
• The metamathematics of ZFC has been extensively studied.
• In [ Tarski's ] view, metamathematics became similar to any mathematical discipline.
• In so doing, they helped found what are now known as metamathematics and model theory.
• String theory is foundational for formal linguistics, computer science, logic, and metamathematics especially proof theory.
• Another work was done by Judson Webb in his 1968 paper " Metamathematics and the Philosophy of Mind ".
• David Hilbert was the first to invoke the term " metamathematics " with regularity ( see Hilbert's program ).
• Becker debated with David Hilbert and Paul Bernays over the role of the potential infinite in Hilbert's formalist metamathematics.
• It is also a gentle and humorous introduction to combinatory logic and the associated metamathematics, built on an elaborate ornithological metaphor.
• The example of ZFC illustrates the importance of distinguishing the metamathematics of a formal system from the statements of the formal system itself.
• Today, metalogic and metamathematics are largely synonymous with each other, and both have been substantially subsumed by mathematical logic in academia.
• Stephen Kleene in his 1952 " Introduction to Metamathematics " describes the " ramified " theory of types this way:
• His Ph . D . thesis was published as the book " Metamathematics, Machines, and Goedel's Proof " by Cambridge University Press in 1994.
• Metamathematics was intimately connected to mathematical logic, so that the early histories of the two fields, during the late 19th and early 20th centuries, largely overlap.
• Beginning in the late 1960s, Chaitin made contributions to algorithmic information theory and metamathematics, in particular a computer-theoretic result equivalent to G鰀el's incompleteness theorem.
• Not only its concepts and results can be mathematized, but they actually can be integrated into mathematics . . . . Tarski destroyed the borderline between metamathematics and mathematics.
• One of these days I'm going to compile a list of the most interesting metamathematics articles . . talk ) 18 : 07, 20 November 2008 ( UTC)