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Contents

• V Full version
• 0 Introduction
• 1 Propositional calculus
• 1.1 Propositions
• 1.2 Semantic entailment
• 1.3 Syntactic implication
• 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
• 3.1 Partial orders
• 3.2 Zorn's lemma and axiom of choice
• 3.3 Bourbaki-Witt theorem*
• 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
• 5.1 Axioms of set theory
• 5.2 Properties of ZF
• 5.3 Picture of the universe
• 6 Cardinals
• 6.1 Definitions
• 6.2 Cardinal arithmetic
• 7 Incompleteness*