set-theoretic love

# set-theoretic

## Definitions

• adjective mathematics Of, relating to or using set theory.

## Etymologies

Sorry, no etymologies found.

## Examples

• First there is a restriction to intuitionistic logic, then a restriction is imposed on the set-theoretic constructions allowed.

Set Theory: Constructive and Intuitionistic ZF

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

Model Theory

• Also, as Boole himself pointed out, his translation from an English argument to its set-theoretic 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.

Model Theory

• Constructive and intuitionistic ZF are based on the same first-order language as classical ZF set theory, thus taking advantage of the simplicity of the set-theoretic language and of our familiarity with it.

Set Theory: Constructive and Intuitionistic ZF

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

Model Theory

• Then he would point out that the original argument paraphrases into a set-theoretic consequence:

Model Theory

• What about “true”, the epsilon of set-theoretic membership, the sign for mereological parthood, the second-order quantifiers, or the quantifier “there are infinitely many”?

Logical Constants

• Weyl had become increasingly critical of the principles underlying the set-theoretic construction of the mathematical continuum.

Hermann Weyl

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

Platonism in Metaphysics

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

Model Theory