I continued reading Peter Smith’s book. I thought about the difference between the completeness and incompleteness theorems in logic. I have a feeling that at least at this level, logic isn’t hard, but that it takes a lot of effort to become familiar with all the definitions (e.g., logical vs non-logical symbols, language, structure, interpretation, model, consequence, expressibility/arithmetical definability, capturability/definability, the two meanings of completeness, theory, effectively axiomatized theory) and notations (e.g., the two meanings of \models, always being clear about meta level vs object level).

I worked problems out of Intermediate Counting & Probability (chapter 2, sets and logic).