: Well-Ordering Theorem; Cantor–Schröder–Bernstein Theorem; Burali-Forti Paradox. Comparison of Popular Introductory Texts
: Defines these fundamental structures strictly within the framework of set theory. A First Course in Mathematical Logic and Set Th...
The curriculum typically follows a progression from basic logical structures to advanced foundational theorems: : Well-Ordering Theorem
While O'Leary's text is comprehensive, other common "First Course" options serve different academic needs: A First Course in Mathematical Logic and Set Theory | Wiley and formal languages
: Introduces symbolic logic, truth tables, and two-column proofs to establish a base for logical inference.
: Covers predicates, quantifiers, and formal languages, providing the necessary syntax for writing mathematical proofs.
: Completeness and Compactness Theorems; Löwenheim–Skolem Theorem.