Axiomatic set theory: ZFC 10 3.1. for any expressions ϕ,ψ. Cardinals 28 5.1. Ordinals 23 5. The axioms 11 3.2. “A revised and corrected republication of Set Theory, originally published in 1971 by Addison-Wesley Publishing Company, Reading, Massachusetts.” Summary: “This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. MAGIC SET THEORY LECTURE NOTES (AUTUMN 2018) DAVID ASPERO´ Contents 1. 1 Elementary Set Theory Notation: fgenclose a set. (For any sets A,B, A× Bis the set of all ordered pairs (a,b) with a∈ Aand b∈ B. The second collection is called a multiset. Now we deﬁne the notion of a sentential formula—an expression which, suitably inter-preted, makes sense. (Georg Cantor) In the previous chapters, we have often encountered "sets", for example, prime numbers form a set, domains in predicate logic form sets as well. The axiomatic method: A crash course in ﬁrst order logic 6 3. This means that {1,2,3} is a set but {1,1,3} is not because 1 appears twice in the second collection. Each So sets can consist of … The set of even integers can be written: {2n : n is an integer} They are not guaran-teed to be comprehensive of the material covered in the course. James Talmage Adams Set Theory \A set is a Many that allows itself to be thought of as a One." Ling 310, adapted from UMass Ling 409, Partee lecture notes March 1, 2006 p. 3 Set Theory Basics.doc Predicate notation. Introduction 2 1.1. Sets are often speciﬁed with curly brace notation. These notes were prepared using notes from the course taught by Uri Avraham, Assaf Hasson, and of course, Matti Rubin. 2.1 Set Theory A set is a collection of distinct objects. The consistency question 19 4. So Expr × Expr is the set of all ordered pairs (ϕ,ψ) with ϕ,ψ expressions.) Example: {x x is a natural number and x < 8} Reading: “the set of all x such that x is a natural number and is less than 8” So the second part of this notation is a prope rty the members of the set share (a condition For any natural number n, let Sn= hn+ 3i. f0;2;4;:::g= fxjxis an even natural numbergbecause two ways of writing These notes for a graduate course in set theory are on their way to be-coming a book. A book of set theory / Charles C Pinter. Ling 409, Partee lecture notes, Lecture 1 September 7, 2005 p. 2 Examples: the set of students in this room; the English alphabet may be viewed as the set of letters of the English language; the set of natural numbers1; etc. De ning a set formally is a pretty delicate matter, for now, we will be happy f1;2;3g= f3;2;2;1;3gbecause a set is not de ned by order or multiplicity. p. cm. Cynthia Church pro-duced the ﬁrst electronic copy in December 2002. They originated as handwritten notes in a course at the University of Toronto given by Prof. William Weiss. Introduction to Logic and Set Theory-2013-2014 General Course Notes December 2, 2013 These notes were prepared as an aid to the student. ZFC vs PA 17 3.3. Some elementary facts about sets 4 2.

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