Set Theory and Logic: Fundamental Concepts (Notes by Dr. J. Santos) A.1. The notes were written by Sigurd Angenent, starting from an extensive collection of notes and problems compiled by Joel Robbin. Definition. Introduction 2 1.1. They originated as handwritten notes in a course at the University of Toronto given by Prof. William Weiss. Primitive Concepts. This chapter will be devoted to understanding set theory, relations, functions. For any natural number n, let Sn= hn+ 3i. 1.1 Sets Mathematicians over the last two centuries have been used to the idea of considering a collection of The proof that p = t in Chapter 34 is based upon notes of Fremlin and a thesis of ... Models of set theory .....160 15. A set is an unordered collection of distinct objects. for any expressions ϕ,ψ. So sets can consist of … A set can be defined by simply listing its members inside curly braces. James Talmage Adams The axiomatic method: A crash course in first order logic 6 3. Lecture Notes 1 Basic Probability • Set Theory • Elements of Probability • Conditional probability • Sequential Calculation of Probability • Total Probability and Bayes Rule • Independence • Counting EE 178/278A: Basic Probability Page 1–1 Set Theory Basics • A set is a … Ling 310, adapted from UMass Ling 409, Partee lecture notes March 1, 2006 p. 3 Set Theory Basics.doc Predicate notation. This is the basic set theory that we follow in set theoretic topology. View full-text (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. DRAFT 2. x2Adenotes xis an element of A. The consistency question 19 4. Axiomatic set theory: ZFC 10 3.1. To denote membership we These notes for a graduate course in set theory are on their way to be-coming a book. Cardinals 28 5.1. f0;2;4;:::g= fxjxis an even natural numbergbecause two ways of writing a set are equivalent. Ordinals 23 5. ZFC vs PA 17 3.3. 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 4 CS 441 Discrete mathematics for CS M. Hauskrecht Equality Definition: Two sets are equal if and only if they have the same elements. Set Theory \A set is a Many that allows itself to be thought of as a One." set theory and forcing lecture notes jean-louiskrivine translated by: christian rosendal typeset by: jessica schirle Now we define the notion of a sentential formula—an expression which, suitably inter-preted, makes sense. Primitive Concepts. De ning a set formally is a pretty delicate matter, for now, we will be happy For example, the set {2,4,17,23} is the same as the set {17,4,23,2}. Some elementary facts about sets 4 2. 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. Ling 310, adapted from UMass Ling 409, Partee lecture notes March 1, 2006 p. 3 Set Theory Basics.doc Predicate notation. Example: • {1,2,3} = {3,1,2} = {1,2,1,3,2} Note: Duplicates don't contribute anythi ng new to a set, so remove them. ;is the empty set. 1 Elementary Set Theory Notation: fgenclose a set. The objects in a set are called the elements, or members, of the set. So Expr × Expr is the set of all ordered pairs (ϕ,ψ) with ϕ,ψ expressions.) Set Theory and Logic: Fundamental Concepts (Notes by Dr. J. Santos) A.1. An Introduction to Elementary Set Theory Guram Bezhanishvili and Eachan Landreth 1 Introduction In this project we will learn elementary set theory from the original historical sources by two key gures in the development of set theory, Georg Cantor (1845{1918) and Richard Dedekind (1831{1916). In mathematics, the notion of a set is a primitive notion. That is, we admit, as a starting point, the existence of certain objects (which we call sets), which we won’t define, but which we assume satisfy some In mathematics, the notion of a set is a primitive notion. We start with the basic set theory. 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 MAGIC SET THEORY LECTURE NOTES (AUTUMN 2018) DAVID ASPERO´ Contents 1. LECTURES ON SET THEORY J. Donald Monk March 11, 2019 i. The LATEX and Python les which were used to produce these notes are available at the following web site The axioms 11 3.2. (For any sets A,B, A× Bis the set of all ordered pairs (a,b) with a∈ Aand b∈ B. It is a lecture note on a axiomatics set theory, ZF set theory with AC, in short ZFC.

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