MTH303: (Set Theory and Logic)

        [Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

• Propositional logic: symbolic logic, inference, replacement, proof methods.
• First-order logic: languages, substitution, syntactics, proof methods.
• Set theory: sets and elements, set operations, sets within sets, families of sets
• Relations and Functions: relations, equivalence relations, partial orders, functions, injections and surjections, images and inverse images
• Axiomatic set theory: axioms, natural numbers, integers and rational numbers, mathematical induction, axiomatic real numbers. Finite, countable and uncountable sets.
• Axiom of Choice: Zorn’s lemma, Well-ordering, existence of real number system.

Additional Topics:

Ordinals and Cardinals: ordinal numbers, cardinal numbers, large cardinals. Godel’s Completeness and Incompleteness theorems

Reference Texts:

1. Michael L. O’Leary: A First Course in Mathematical Logic and Set Theory
2. P. T. Johnstone: Notes on Logic and Set Theory.
3. Yu. I. Manin: A Course in Mathematical Logic for Mathematicians.