6
votes
1answer
567 views

Relationship between propositional logic, first-order logic, second-order logic higher-order logic, and type theory

I understand there is propositional logic, first-order logic, second-order logic higher-order logic, and type theory, where the latter logics are extensions of the former logics. Can someone explain ...
4
votes
2answers
141 views

Is higher order type theory the same as higher order logic?

The internal language of a topos is higher order intuitionistic type theory (or logic). Here the higher order simply refers to allowing function types. In mathematical logic we have higher-order ...
2
votes
0answers
77 views

Introductory text about different stratification methods in higher-order logic and set theory

Could someone recommend me a good overview text about stratification of predicates, comprehension axioms, and other methods of avoiding the paradoxes in untyped or only loosely/relatively typed ...