"स्वयंसिद्धों की सूची" सम्पादित करें

यहाँ पर सभी प्रकार के [[अभिगृहीत|स्वयंसिद्धों]] (axioms) की सूची दी गयी है। 

== [[जर्मेलो-फ्रंकेल स्वयंसिद्ध]] (Zermelo-Frankel axioms) ==
ये समसामयिक गणित एवं [[सम्मुच्चय सिद्धान्त]] के लिये 'मानक' स्वयंसिद्ध हैं। 

* [[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]]

 [[जर्मेलो का समुच्चय सिद्धान्त]] भी देखें।

== [[विकल्प के स्वयंसिद्ध]] (Axiom of choice / AC) ==

=== AC के तुल्य ===
* [[Hausdorff maximality theorem]]
* [[Well-ordering principle]]
* [[Zorn's lemma]]

=== AC से कमजोर ===
* [[Axiom of countable choice]]
* [[Axiom of dependent choice]]
* [[Boolean prime ideal theorem]]
* [[Axiom of uniformization]]

=== Alternates incompatible with AC ===
* [[Axiom of real determinacy]]

== [[गणितीय तर्कशास्त्र|गणितीय तर्क]] (mathematical logic) के अन्य स्वयंसिद्ध ==

* [[Von Neumann-Bernays-Gödel axioms]]
* [[Continuum hypothesis]] and [[Continuum hypothesis#The generalized continuum hypothesis|its generalization]]
* [[Freiling's axiom of symmetry]]
* [[Axiom of determinacy]]
* [[Axiom of projective determinacy]]
* [[Martin's axiom]]
* [[Axiom of constructibility]]
* [[Rank-into-rank]]
* [[Kripke-Platek axioms]]

== [[ज्यामिति]] ==

* [[Parallel postulate]] 
* [[Birkhoff's axioms]]
* [[Hilbert's axioms]]
* [[Tarski's axioms]]

== विविध ==
* [[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]])

[[श्रेणी:सूचियाँ]]
[[श्रेणी:गणित]]
[[श्रेणी:तर्कशास्त्र]]