Now we define the notion of a sentential formula—an expression which, suitably inter-preted, makes sense. Cardinals 28 5.1. 1 Elementary Set Theory Notation: fgenclose a set. MAGIC SET THEORY LECTURE NOTES (AUTUMN 2018) DAVID ASPERO´ Contents 1. f0;2;4;:::g= fxjxis an even natural numbergbecause two ways of writing For any natural number n, let Sn= hn+ 3i. Some elementary facts about sets 4 2. for any expressions ϕ,ψ. (For any sets A,B, A× Bis the set of all ordered pairs (a,b) with a∈ Aand b∈ B. This means that {1,2,3} is a set but {1,1,3} is not because 1 appears twice in the second collection. 2.1 Set Theory A set is a collection of distinct objects. “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. They originated as handwritten notes in a course at the University of Toronto given by Prof. William Weiss. Ling 310, adapted from UMass Ling 409, Partee lecture notes March 1, 2006 p. 3 Set Theory Basics.doc Predicate notation. These notes for a graduate course in set theory are on their way to be-coming a book. So Expr × Expr is the set of all ordered pairs (ϕ,ψ) with ϕ,ψ expressions.) A book of set theory / Charles C Pinter. f1;2;3g= f3;2;2;1;3gbecause a set is not de ned by order or multiplicity. De ning a set formally is a pretty delicate matter, for now, we will be happy Sets are often specified with curly brace notation. James Talmage Adams p. cm. Cynthia Church pro-duced the first electronic copy in December 2002. ZFC vs PA 17 3.3. The set of even integers can be written: {2n : n is an integer} The consistency question 19 4. The axiomatic method: A crash course in first order logic 6 3. Ordinals 23 5. So sets can consist of … Axiomatic set theory: ZFC 10 3.1. Introduction to Logic and Set Theory-2013-2014 General Course Notes December 2, 2013 These notes were prepared as an aid to the student. They are not guaran-teed to be comprehensive of the material covered in the course. These notes were prepared using notes from the course taught by Uri Avraham, Assaf Hasson, and of course, Matti Rubin. (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. Introduction 2 1.1. 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 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. The second collection is called a multiset. Set Theory \A set is a Many that allows itself to be thought of as a One." The axioms 11 3.2. Each