Science Fair Project Encyclopedia
List of axioms
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.
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Zermelo-Frankel axioms
These are the de facto standard axioms for contemporary mathematics
- 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.
Axiom of choice
With the Zermelo-Frankel axioms above, this makes up the system ZFC in which most mathematics is potentially formalisable
Equivalents of AC
Weaker than AC
Alternates incompatible with AC
Other axioms of mathematical logic
- 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
Geometry
Other axioms
10-26-2009 08:16:03
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details