Set theory is the branch of mathematical logic that studies sets, which informally are collections of objects. They are not guaran-teed to be comprehensive of the material covered in the course. For its applications in topology, analysis, algebra, AI, databases. It is written for the upper level undergraduate or beginning graduate students to help them prepare for advanced study in set theory and mathematical logic as well as other areas of mathematics, such as analysis, topology, and algebra. These notes were prepared using notes from the course taught by Uri Avraham, Assaf Hasson, and of course, Matti Rubin. ha;bi= ffag;fa;bgg Theorem 1.5. ha;bi= hc;dii a= cand b= d. Proof. 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. Set theory is a basis of modern mathematics, and notions of set theory are used in all formal descriptions. De nition 1.7 (Ordered Pair). So a= c= d, in particular, a= cand b= d. 2. 2. This book provides an introduction to axiomatic set theory and descriptive set theory. It only remains to de ne ha;biin terms of set theory. Set Theory is indivisible from Logic where Computer Science has its roots. This book describes some basic ideas in set theory, model theory, proof theory, and recursion theory; these are all parts of what is called mathematical logic. Because the foundations of mathematics is relevant to philosophy. An Introduction To Set Theory. 3. It is also deals with Quine's systems. Then ffag;fa;bgg= ffag;fa;agg= ffag;fagg= ffagg Since ffagg= ffcg;fc;dggwe must have fag= fcgand fag= fc;dg. 2 2. The notion of set is taken as “undefined”, “primitive”, or “basic”, so we don’t try to define what a set is, but we can give an informal description, describe important properties of sets, and give examples. Suppose a= b. Clearly if a= cand b= dthen ha;bi= ffag;fa;bgg= ffcg;fc;dgg= hc;di 1. In the first edition of this book, “studies in logic and the foundations of mathematics,” the set theory is discussed in its original form. Selecting the material for presentation in this book often came down to deciding how much detail should be provided when explaining concepts and what constitutes a reasonable logical gap which can be independently ﬁlled in by the reader. The semantics of Predicate Logic is defined in terms of Set Theory. A set theory textbook can cover a vast amount of material depending on the mathematical background of the readers it was designed for. (Sentence 1 tells us they are among the things that are mortal.) It has been and is likely to continue to be a a source of fundamental ideas in Computer Science from theory to practice; Computer Science, being a science of the arti cial, has had many of its constructs and ideas inspired by Set Theory. There are three reasons one might want to read about this: 1. As an introduction to logic. Fido Sue Fred Aristotle Bob The collection of things in the world that are mortal The collection of things in the world that are men.