We discussed the connection between logic and language, and the role of predicates in particular. We practiced formalizing three of the axioms of set theory (the axioms of extensionality, empty set, and pairing).

1. How finite sequences are defined in set theory.
2. The fact that if $A$ is an alphabet of size $\leq \kappa$, $\kappa$ infinite, then there are $\leq \kappa$ finite sequences that are constructible from the alphabet $A$. This implies that there are only countably many formulas in a given countable alphabet.
3. The types of symbols needed to express the Goldbach Conjecture: variables, logical symbols, equality, nonlogical symbols (constant symbols, operation symbols, predicate symbols), and punctuation symbols.
4. The types of symbols needed to express the continuity of a function: variables, logical symbols, equality, nonlogical symbols (constant symbols, operation symbols, predicate symbols), and punctuation symbols.
5. The construction of formulas in a 1-sorted language, $\mathcal{L}$. We completed the description of $\mathcal{L}$-terms.

1. Terms.
2. Atomic formulas.
3. Formulas and sentences.
4. Formula trees.

We discussed:

1. The language of Sentential Logic (= propositional logic = 0th-order logic). (Introduced by Stoic philosopher Chryssipus ~250 BCE.)
2. Sentential formulas. Wffs.
3. Formula trees.
4. Truth assignments. Tautologies and contradictions.

1. Unique readability of propositional formulas.
2. Completeness of sets of connectives.

1. Completeness of sets of connectives.
2. Disjunctive Normal Form..