Axiomatic system

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