مستخدم:Chaos/قائمة البدهيات
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.
Zermelo-Frankel axioms[عدل]
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.
بدهية الاختيار[عدل]
With the Zermelo-Frankel axioms above, this makes up the system ZFC in which most mathematics is potentially formalisable.
Equivalents of AC[عدل]
Weaker than AC[عدل]
- Axiom of countable choice
- Axiom of dependent choice
- Boolean prime ideal theorem
- Axiom of uniformization
Alternates incompatible with AC[عدل]
بدهيات أخرى منطق رياضي[عدل]
- 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
هندسة رياضية[عدل]
بدهيات أخرى[عدل]
- 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)
{{بوابة رياضيات}} [[:تصنيف:بديهيات رياضية|*]] [[:تصنيف:قوائم رياضية]]