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What is an axiomatization?

What is an axiomatization? Here are some definitions.

Noun
  1. The reduction of some system or concept to a set of axioms.
  2. The result of establishing a concept within a system of axioms; axiomatic system.
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Examples
The axiomatization of set theory formed the foundations, mathematically, of everything else.
Frege asked about Hilbert's claim that his axiomatization provides definitions of the primitives of geometry, so that the very same sentences serve as axioms and definition.

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