Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 verb Simple past tense and past participle of
axiomatize .
Etymologies
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Examples

For Hilbert on the other hand, at least in the context of axiomatized geometry, the logical relations simply are the formallydescribable relations, since they have entirely to do with the structure exhibited by the sentences in question, or equivalently with the

˜Ï™ in place of set abstraction, it follows that the parthood relation axiomatized by GEM has essentially the same properties as the inclusion relation in standard set theory.

Aristotle's account of proof as demonstrative argument fits very well to the structure of ancient geometry as axiomatized in Euclid.

What GÃ¶del showed is that, for any consistent, recursively axiomatized formal system, F, strong enough for arithmetic, there are truths expressible in purely arithmetical language which are not provable in F.

There's a technical solution to Skolem's Paradox which explains why the LÃ¶wenheimSkolem Theorems pose no problems for either naive forms of settheoretic realism or various forms of axiomatized set theory.

It's important to emphasize that this analysis also explains why Skolem's Paradox doesn't introduce contradictions into various forms of axiomatized set theory, even when these axiomatizations are themselves understood formalistically or modeltheoretically.

Given this, our only real option is to fall back on some form of axiomatized set theory, and the only respectable way to understand our axioms is algebraically (since understanding them intuitively would amount to falling back into our previously discredited naivetÃ©).

Dcomplete, that is, they all may be axiomatized by axioms and the rule of condensed detachment.

Economic theories have been axiomatized, and articles and books of economics are full of theorems.

The NagelSchaffner approach to theory reduction assumes a syntactic account of theory structure such that they are axiomatized systems formalizable in first order predicate calculus.
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