axiomatic set theory การใช้

• Zermelo set theory was the first axiomatic set theory.
• Accepting only the axiom schema of specification was the beginning of axiomatic set theory.
• On the other hand, among axiomatic set theories, ZFC is comparatively weak.
• This paradox is avoided in axiomatic set theory.
• In 1908, Ernst Zermelo proposed the first axiomatic set theory, Zermelo set theory.
• During the 20th Century, it became the standard to build mathematical theories on axiomatic set theory.
• In some systems of axiomatic set theory, relations are extended to classes, which are generalizations of sets.
• Likewise, an axiomatic set theory is not necessarily consistent, i . e . not necessarily free of paradoxes.
• It is Tarski's axiom that distinguishes "'TG "'from other axiomatic set theories.
• "' ST "'reveals how type theory can be made very similar to axiomatic set theory.
• As such, the construction is rooted in axiomatic set theory, and is closely related to the Zermelo Fraenkel axioms.
• Also in 1908, Ernst Zermelo proposed " definite " property and the first axiomatic set theory, Zermelo set theory.
• Zorn s lemma is an alternative expression of the axiom of choice, and thus a subject of interest in axiomatic set theory.
• That a set can capture the notion of the extension of anything is the idea behind the axiom of extensionality in axiomatic set theory.
• Le [
  niewski was also a radical nominalist : he rejected axiomatic set theory at a time when that theory was in full flower.
• The PFL translation of the canonical axiomatic set theory ZFC is not difficult, as no ZFC axiom requires more than 6 quantified variables.
• This definition must be abandoned in ZF and related systems of axiomatic set theory because these equivalence classes are too large to form a set.
• He is known for his contributions to axiomatic set theory, especially his addition to Ernst Zermelo's axioms which resulted in Zermelo Fraenkel axioms.
• An appendix sets out a new approach to axiomatic set theory, now called Morse Kelley set theory, that builds on Von Neumann Bernays G鰀el set theory.
• In 1908, two ways of avoiding the paradox were proposed, Russell's type theory and the Zermelo set theory, the first constructed axiomatic set theory.