Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 adjective mathematics Of, relating to or using
set theory .
Etymologies
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Examples

First there is a restriction to intuitionistic logic, then a restriction is imposed on the settheoretic constructions allowed.

But in a broader sense, model theory is the study of the interpretation of any language, formal or natural, by means of settheoretic structures, with Alfred Tarski's truth definition as a paradigm.

Also, as Boole himself pointed out, his translation from an English argument to its settheoretic form requires us to believe that for every property used in the argument, there is a corresponding class of all the things that have the property.

Constructive and intuitionistic ZF are based on the same firstorder language as classical ZF set theory, thus taking advantage of the simplicity of the settheoretic language and of our familiarity with it.

But it is a serious hypothesis that in fact our mental representations have a good deal in common with simple settheoretic structures, so that they are ˜models™ in the modeltheoretic sense too.

Then he would point out that the original argument paraphrases into a settheoretic consequence:

What about “true”, the epsilon of settheoretic membership, the sign for mereological parthood, the secondorder quantifiers, or the quantifier “there are infinitely many”?

Weyl had become increasingly critical of the principles underlying the settheoretic construction of the mathematical continuum.

But in fact, there are infinitely many different kinds of settheoretic structures, and platonists can argue that physicalistic views like Maddy's are incompatible with this.

For example in Boole's case the settheoretic consequences that he relies on are all easily provable by formal proofs in firstorder logic, not even using any settheoretic axioms; and by the completeness theorem (see the entry on classical logic) the same is true for firstorder logic.
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