The first five chapters of Marker’s Model Theory will satisfy
syntax and semantics for propositional and first-order classical logic
and some information about type theory in the context of model theory. I know it doesn’t satisfy all of your requirements, but it is a seriously good book with an excellent learning curve. I took a semester course covering the first three chapters in undergrad. It almost convinced me to work in mathematical logic, but sadly economic incentives trumped aesthetic ones.
The first five chapters of Marker’s Model Theory will satisfy
and some information about type theory in the context of model theory. I know it doesn’t satisfy all of your requirements, but it is a seriously good book with an excellent learning curve. I took a semester course covering the first three chapters in undergrad. It almost convinced me to work in mathematical logic, but sadly economic incentives trumped aesthetic ones.