# Part II - Logic and Set Theory

## Lectured by I. B. Leader, Lent 2015

These notes are not endorsed by the lecturers, and I have modified them (often significantly) after lectures. They are nowhere near accurate representations of what was actually lectured, and in particular, all errors are almost surely mine.

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# Contents

- V Full version
- 0 Introduction
- 1 Propositional calculus
- 2 Well-orderings and ordinals
- 2.1 Well-orderings
- 2.2 New well-orderings from old
- 2.3 Ordinals
- 2.4 Successors and limits
- 2.5 Ordinal arithmetic
- 2.6 Normal functions*
- 3 Posets and Zorn's lemma
- 4 Predicate logic
- 4.1 Language of predicate logic
- 4.2 Semantic entailment
- 4.3 Syntactic implication
- 4.4 Peano Arithmetic
- 4.5 Completeness and categoricity*
- 5 Set theory
- 6 Cardinals
- 7 Incompleteness*