Schedule

Overall, as things stand now, our progression will look like this:

1. complete ``mini" coverage of propositional and predicate calculus (and what it presupposes, e.g., naive set theory), including syntax, semantics, proof theory;
2. logic programming and automated theorem proving (briefly);
3. Gödel's completeness theorem;
4. Skolem-Löwenheim theorem;
5. brief foray into axiomatic set theory (including Cantor's theorem, whether or not first-order logic is sufficient to articulate all of classical mathematics);
6. brief coverage of logics ``beyond" first-order logic (including second-order logic, modal logic);
7. Lindström's theorems;
8. computability (including Turing machines, Register machines, Church's Thesis);
9. uncomputability:
   1. halting problem
   2. undecidability of first-order logic
   3. Gödel's incompleteness theorems
   4. the arithmetic hierarchy
   5. uncomputability through real number parameters, analog shift maps, analog chaotic neural nets, etc.

Exact reading assignments and test dates etc. will be given in class and on the course web page as we progress.