Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 noun The act of making
axiomatic .  noun The act or process of establishing a concept within a system of
axioms .  noun The result of establishing a concept within a system of
axioms ;axiomatic system .
Etymologies
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Examples

This reflects changes within math itself, where formal axiomatization is now out of fashion and things like computer simulation are much more used.
Memetic Suicide, Bryan Caplan  EconLog  Library of Economics and Liberty

There were efforts — by Peano and so on — to come up with definitive axiomatization of mathematics.
Wolfram Blog : Stephen Wolfram on the Quest for Computable Knowledge

Powers: first axiomatization of logic; knowledge of eternal, immaterial entities

Not only did he anticipate Heisenberg's Uncertainty Principle, and set out a finite axiomatization of arithmetic before Peano did, and the basis axiomatic set theory before Zermelo did, but also his notation and terminology were readable and suggestive, giving future logicians a better language to work in than the clunky terms of the Germans.

On the other hand one was familiar with Hilbert's axiomatization of geometry which, although rigorous, did not have the character of artificiality of the constructive theories.

The axiomatization of theories has modified very deeply the style of contemporary mathematical writings.

Another example mentioned by Chevalley is the axiomatization of field theory given by Steinitz in 1910.

According to Huntington (1933), the term “Boolean algebra” was introduced by Sheffer (1913) in the paper where he showed that one could give a fiveequation axiomatization of Boolean algebra using the single fundamental operation of joint exclusion, now known as the Sheffer stroke.

Yet a fourth response was embodied in Ernst Zermelo's 1908 axiomatization of set theory.

Let T be a standard, firstorder axiomatization of set theory.
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