Logic and Set Theory

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Author(s): I. B. Leader, ed. Dexter Chua
Series: Cambridge Mathematical Tripos Part II Lecture Notes
Publisher: University of Cambridge
Year: 2015

Language: English
City: Cambridge
Tags: maths; mathematics; math; advanced; college; university; higher; further; pure; applied; logic; sets; set theory; axiomatic; classical

Introduction
Propositional calculus
Propositions
Semantic entailment
Syntactic implication
Well-orderings and ordinals
Well-orderings
New well-orderings from old
Ordinals
Successors and limits
Ordinal arithmetic
Normal functions*
Posets and Zorn's lemma
Partial orders
Zorn's lemma and axiom of choice
Bourbaki-Witt theorem*
Predicate logic
Language of predicate logic
Semantic entailment
Syntactic implication
Peano Arithmetic
Completeness and categoricity*
Set theory
Axioms of set theory
Properties of ZF
Picture of the universe
Cardinals
Definitions
Cardinal arithmetic
Incompleteness*
Index