: Well-Ordering Theorem; Cantor–Schröder–Bernstein Theorem; Burali-Forti Paradox. Comparison of Popular Introductory Texts
The curriculum typically follows a progression from basic logical structures to advanced foundational theorems: A First Course in Mathematical Logic and Set Th...
: Moves from informal set operations (unions, intersections) to axiomatic set theory (ZFC) . O'Leary is a foundational textbook designed to transition
by Michael L. O'Leary is a foundational textbook designed to transition students from computational mathematics to rigorous proof-writing. It presents symbolic logic not just as an abstract subject, but as the essential framework for structuring mathematical arguments. Core Course Components Key Theorems Covered While O'Leary's text is comprehensive,
: Includes the construction of number systems (naturals, ordinals, cardinals) and concludes with an introduction to model theory . Key Theorems Covered
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
: Defines these fundamental structures strictly within the framework of set theory.