Übersetzung für 'metamathematics' von Englisch nach Deutsch

metamathematics [treated as sg.]

Metamathematik {f}acad.math.

• Metamathematics is the study of mathematics itself using mathematical methods.
• The metamathematics of Zermelo–Fraenkel set theory has been extensively studied.
• It is also a gentle and humorous introduction to combinatory logic and the associated metamathematics, built on an elaborate ornithological metaphor.
• In so doing, they helped found what is now known as metamathematics and model theory.
• Gödel's incompleteness theorems show that Hilbert's program cannot be realized: if a consistent recursively enumerable theory is strong enough to formalize its own metamathematics (whether something is a proof or not), i.e.

• The paradox is ordinarily used to motivate the importance of distinguishing carefully between mathematics and metamathematics.
• His semantic methods, which culminated in the model theory he and a number of his Berkeley students developed in the 1950s and 60s, radically transformed Hilbert's proof-theoretic metamathematics.
• Becker debated with David Hilbert and Paul Bernays over the role of the potential infinite in Hilbert's formalist metamathematics.
• The mental capabilities of Minds are described in "Excession" to be vast enough to run entire universe-simulations inside their own imaginations, exploring metamathical (a fictional branch of metamathematics) scenarios, an activity addictive enough to cause some Minds to totally withdraw from caring about our own physical reality into "Infinite Fun Space", their own, ironic and understated term for this sort of activity.
• Where the starting point for the metamathematics of Zermelo-Fraenkel set theory is the easy-to-formalize intuition of the cumulative hierarchy, the non-well-foundedness of NF and NFU makes this intuition not directly applicable.

• Niebergall’s research has centered on the metamathematics of formal theories related to mereology and infinity.
• David Hilbert founded metamathematics as a discipline for discussing formal systems.
• In modern nomenclature, "meta"- can also serve as a prefix meaning self-referential, as a field of study or endeavor (metatheory: theory about a theory; metamathematics: mathematical theories about mathematics; meta-axiomatics or meta-axiomaticity: axioms about axiomatic systems; metahumor: joking about the ways humor is expressed; etc.).