14. Godel Theorems
Godel's incompleteness theorems show that sufficiently expressive formal systems have inherent limits, especially when they are able to represent basic arithmetic. The chapter begins with arithmetization of syntax, where formulas, proofs, and derivations are encoded as natural numbers, allowing a formal system to speak about its own syntactic objects. The first incompleteness theorem is then introduced, showing that any consistent and sufficiently strong formal system contains true arithmetic statements that...