Difference between revisions of "Axiomatic system"
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Latest revision as of 04:53, 21 April 2016
In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems.
Description
A mathematical theory consists of an axiomatic system and all its derived theorems.
Formal system
An axiomatic system that is completely described is a special kind of formal system; usually though, the effort towards complete formalisation brings diminishing returns in certainty, and a lack of readability for humans.
Formal theory
A formal theory typically means an axiomatic system, for example formulated within model theory.
Formal proof
A formal proof is a complete rendition of a mathematical proof within a formal system.
See also
- Axiom
- Formal proof
- Formal system
- Formal theory
- Gödel's incompleteness theorems
- Mathematical proof
- Mathematical theory
- Mathematics
- Theorem
External links
- Axiomatic system @ Wikipedia
