مستخدم:Chaos/قائمة البدهيات

من ويكيبيديا، الموسوعة الحرة

This is a list of axioms as that term is understood in mathematics, by Wikipedia page. In epistemology, the word axiom is understood differently; see axiom and self-evidence. Individual axioms are almost always part of a larger axiomatic system.

فهرست

[تحرير] Zermelo-Frankel axioms

These are the de facto standard axioms for contemporary mathematics or set theory. They can be easily adapted to analogous theories, such as mereology.

  • Axiom of extensionality
  • Axiom of empty set
  • Axiom of pairing
  • Axiom of union
  • Axiom of infinity
  • Axiom schema of replacement
  • Axiom of power set
  • Axiom of regularity
  • Axiom of separation
  • Axiom schema of specification

See also Zermelo set theory.

[تحرير] بدهية الاختيار

With the Zermelo-Frankel axioms above, this makes up the system ZFC in which most mathematics is potentially formalisable.

[تحرير] Equivalents of AC

  • Hausdorff maximality theorem
  • Well-ordering principle
  • Zorn's lemma

[تحرير] Weaker than AC

  • Axiom of countable choice
  • Axiom of dependent choice
  • Boolean prime ideal theorem
  • Axiom of uniformization

[تحرير] Alternates incompatible with AC

  • Axiom of real determinacy

[تحرير] بدهيات أخرى منطق رياضي

  • Von Neumann-Bernays-Gödel axioms
  • Continuum hypothesis
  • Generalized continuum hypothesis
  • Freiling's axiom of symmetry
  • Axiom of determinacy
  • Axiom of projective determinacy
  • Martin's axiom
  • Axiom of constructibility
  • Rank-into-rank
  • Kripke-Platek axioms

[تحرير] هندسة رياضية

  • Parallel postulate
  • Birkhoff's axioms
  • Hilbert's axioms
  • Tarski's axioms

[تحرير] بدهيات أخرى

  • Axiom of Archimedes (real number)
  • Axiom of countability (topology)
  • Fundamental axiom of analysis (real analysis)
  • Gluing axiom (sheaf theory)
  • Haag-Kastler axioms (quantum field theory)
  • Huzita's axioms (origami)
  • Kuratowski closure axioms (topology)
  • Peano's axioms (natural numbers)
  • Probability axioms
  • Separation axiom (topology)
  • Wightman axioms (quantum field theory)