Linked from

The 35 pages that link to Type theory, each with the reason it gives.

• Set theoryCompared with: It offers a foundational alternative to treating all mathematical objects as sets.

• Zermelo–Fraenkel set theoryCompared with: It is a foundational alternative that avoids treating every object as a set.

• Category theoryCompared with: Type theory offers a distinct foundation that can also express categorical structures.

• Mathematical logicCompared with: It offers an alternative foundational framework in which types can encode propositions and proofs.

• Ernst ZermeloCompared with: It offers a foundational alternative to Zermelo’s set-based axiomatic approach.

• Cumulative hierarchyCompared with: Its stratification avoids treating all mathematical objects as levels of one cumulative set universe.

• Second-order logicCompared with: Some type theories encode higher-order reasoning through typed functions and propositions.

• Personality traitCompared with: Trait models usually describe degrees, not sharply separated personality types.

• ElementCompared with: Type membership resembles set membership but belongs to a different formal framework.

• Axiomatic systemCompared with: It can serve as a foundation for mathematics through typed constructions rather than set-theoretic axioms.

• Axiom of Power SetCompared with: Many type-theoretic foundations represent collections without adopting this set-existence axiom.

• Axiom of Empty SetCompared with: Some type theories treat empty types rather than assuming an empty set as an axiom.

• Universe (mathematics and logic)Compared with: Type theories can organize objects into levels instead of placing everything in one domain.