My Notes | Allen's Corner of the World

Logic

Propositional Logic – Expressive completeness, soundness, and completeness
First Order Logic – Various proof systems, soundness and completeness
Modal Logic – Propositional modal logics and their applicational variants, completeness of K, and (a little bit of) first order modal logic

Automata, Computability, and Complexity – Finite Automaton, Context-Tree Languages, Turing Machines, Decidability and Reducibility, and (a little bit of) complexity theory
Arithmetic and Incompleteness – Recursive functions, arithmetization of syntax, undecidability and incompleteness theorems of arithmetic, and nonstandard models

Type Theory – Untyped λ-calculus, systems on the Lambda cube, Church encodings, and embedding of Intuitionist Logic in λC
Set Theory – Naive set theory (incomplete)
Paradoxes – The semantic and set-theoretic paradoxes, Sorities, Knower variants, and the Inclosure Schema