Topics

Focused deep-dives into individual results and themes that build on the core logic pages. Where the main pages survey whole systems, these notes zoom in on a single landmark.

Contents

1. Gödel's Incompleteness Theorems — the two limitative theorems of 1931: any consistent, effectively axiomatized theory interpreting arithmetic is incomplete and cannot prove its own consistency; the machinery of Gödel numbering, representability, and the diagonal lemma; and the related results of Tarski, Church–Turing, Rosser, and Löb.

Reading order

These are self-contained but assume the syntax/semantics vocabulary of first-order logic. Read Gödel's Incompleteness Theorems after first-order logic and ideally alongside set theory, where the same independence phenomena recur for the Continuum Hypothesis and the Axiom of Choice.