Titlebook: Set Theory; With an Introduction Abhijit Dasgupta Textbook 2014 Springer Science+Business Media New York 2014 Cantor‘s Theorem.Dedekind‘s T

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Cardinals: Finite, Countable, and Uncountablers, from which the Dedekind–Peano axioms are derived as theorems. Dedekind infinite sets and reflexive cardinals are also defined. It then presents the axiom of!choiceAxiom of Choice and contrasts it with effective!choiceeffective choice, using the notion of effectivenesseffectiveness informally. Th

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Well-Orders and Ordinalsvon Neumann ordinals. We cover the basic ordinal operations of sum and product, transfinite induction and recursion, uniqueness of isomorphisms and ranks, unique representation of well-orders by initial sets of ordinals, the comparability theorem for well-orders, the division algorithm, remainder or

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Postscript II: Infinitary Combinatoricsded to be a link for the reader to begin further study in the area. We indicate how the obvious generalizations of three separate topics of the last chapter, namely short orders, König’s Infinity Lemma, and Ramsey’s Theorem, converge naturally to the notion of a ., an example of a large cardinal. In

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The Heine–Borel and Baire Category Theoremsc proof that . is uncountable. Other topics focus on measure and category: Lebesgue measurable sets, Baire category, the perfect set property for . sets, the Banach–Mazur game and Baire property, and the Vitali and Bernstein constructions.

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Well-Orders and Ordinalsnks, unique representation of well-orders by initial sets of ordinals, the comparability theorem for well-orders, the division algorithm, remainder ordinals, ordinal exponentiation, and the Cantor Normal Form.