It aims to scratch the tip of the surface of the philosophy of set theory. Sentential logic we go into the mathematical theory of the simplest logical notions. Set theory for computer science university of cambridge. They are not guaranteed to be comprehensive of the material covered in the course. Give several examples of a set x such that each element of x is a subset of x. An overview of logic, proofs, set theory, and functions. There are three reasons one might want to read about this.
Mathematics are constr ucted from the axi oms of logic and the axi oms of class and set t heory. Logic and set theory virginia commonwealth university. Ellermeyer august 18, 2000 set theory membership a setis a welldefined collection of objects. If the object x is a member of the set a, then we write x a which is read as x is a member of aorx belongstoaorx is in aorx is an. Center for the mathematics of uncertainty an introduction to the mathematics of uncertainty including set theory, logic, probability, fuzzy sets, rough sets, and evidence theory. Mathematical logic is a branch of mathematics which is mainly concerned with the relationship between semantic concepts i. Logic and set theory a rigorous analysis of set theory belongs to the foundations of mathematics and mathematical logic. By the end of this book, students reading it might have a sense of.
No student is expected to really benefit from these notes unless they have regularly attended the lectures. The course introduces some basic notions that will be needed as background for most of the computer science courses. Psu math relays logic and set theory 2016 there are 33 questions. Motivation when you start reading these notes, the first thing you should be asking yourselves is what is set theory and why is it relevant.
Select the letter of the most appropriate answer and shade in the corresponding region on the answer sheet. The study of these topics is, in itself, a formidable task. For example, a deck of cards, every student enrolled in. It has been and is likely to continue to be a a source of fundamental ideas in computer science from theory to practice. Though aimed at a nonmathematical audience in particular, students of philosophy and computer science, it is rigorous. In this introduction to set theory and logic, the author discusses first order logic, and gives a rigorous axiomatic presentation of zermelofraenkel set theory. Basic set theory a set is a many that allows itself to be thought of as a one. This is being written as a textbook for math 502, logic and set theory, and.
Chapter 1 logic and set theory to criticize mathematics for its abstraction is to miss the point entirely. This book describes some basic ideas in set theory, model theory, proof theory, and recursion theory. However, most of the time, we only have an intuitive picture of what set theory should look like there are sets, we can take intersections, unions, intersections and subsets. Introduction to set theory and logic literaturverz. Set theory and logic is the result of a course of lectures for advanced undergraduates, developed at oberlin college for the purpose of introducing students to the conceptual foundations of mathematics. Proof, sets, and logic department of mathematics boise state.
Mathematics, specifically the real number system, is approached as a unity whose operations can be logically ordered through axioms. About the open logic project the open logic text is an opensource, collaborative textbook of formal metalogic and formal methods, starting at an intermediate level i. Pdf list of books of logic and set theory researchgate. For its applications in topology, analysis, algebra, ai, databases. Remember, no credit is given for any marks on the answer sheet except the. Set theory and logic why understand set theory and logic applications. Select the letter of the most appropriate answer and shade in the corresponding region of the answer sheet. The omitting types theorem of infinitary logic is used to prove that every small. Introduction to logic and set theory 202014 bgu math. The language of set theory can be used to define nearly all mathematical objects. Though propositional logic will prove a useful tool to describe certain aspects of meaning, like the reasoning in 1, it is a blunt. Computer science, being a science of the arti cial, has had many of its constructs and ideas inspired by set theory. Like logic, the subject of sets is rich and interesting for its own sake.
We will return to sets as an object of study in chapters 4 and 5. It will be suitable for all mathematics undergraduates coming to the subject for the first time. Applying formalized logic to analysis a biographical memoir written for the national academy of sciences by martin davis and edmond schonberg pdf file jacob t. Set theory and logic supplementary materials math 103. Gcse tutorial set notation and venn diagrams shading, intersections higher and foundation duration. Set theory is indivisible from logic where computer science has its roots. Psu math relays logic and set theory 2016 c wars or. This book has been reprinted with the cooperation of kyung moon publishers, south korea. The book is based on lectures given at the university of cambridge and covers the basic concepts of logic. Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects. If the correct answer is not one of the choices, mark e on teh answer sheet. 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. Any object which is in a set is called a member of the set.
It is designed for a onesemester course in set theory at the advanced undergraduate or beginning graduate level. The significance of a demand for constructive proofs can be evaluated only after a certain amount of experience with mathematical logic has been obtained. Highlighting the applications and notations of basic mathematical concepts within the framework of logic and set theory, a first course in mathematical logic and set theory introduces how logic is used to prepare and structure proofs and solve more. A book of set theory, first published by dover publications, inc. Basic set theory lx 502 semantics i september 11, 2008 1. Leader, lentterm 2005, 2010 chapter 1 propositional logic 1 chapter 2 wellorderings and ordinals 7 chapter 3 posets and zorns lemma 16 chapter 4 predicate logic 24 chapter 5 set theory 34 chapter 6 cardinals 43 bonus lecture incompleteness examples sheets prerequisites.
Complex issues arise in set theory more than any other area of pure mathematics. A mathematical introduction to the theory and applications of logic and set theory with an emphasis on writing proofs. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. A first course in mathematical logic and set theory. He includes many methodological remarks and explanations, and demonstrates how the basic concepts of mathematics can be reduced to set theory.
For those of you new to abstract mathematics elementary does not mean simple though much of the material. This course provides an introduction to the basic concepts and results of mathematical logic and set theory. These notes were prepared using notes from the course taught by uri avraham, assaf hasson, and of course, matti rubin. Schwartz january 9, 1930 march 2, 2009 a celebration of the life of jacob t. Georg cantor this chapter introduces set theory, mathematical induction, and formalizes the notion of mathematical functions. We cant think of examples of the use of intransitive verbs. In mathematics, the notion of a set is a primitive notion. Introduction to logic and set theory202014 general course notes december 2, 20 these notes were prepared as an aid to the student. Describe how you would structure a key word search to find the information described. Pdf current theories of sets as zermelo faenkel set theory are usually presented as the combination of two distinct kinds of principles. The axiom of pair, the axiom of union, and the axiom of.
Although elementary set theory is wellknown and straightforward, the modern subject, axiomatic set theory, is both conceptually more di. Set theory is a very general but still entirely exact theory of objects called sets. If you concentrate too closely on too limited an application of a mathematical idea, you rob the mathematician of his most important tools. Pdf construction of a set of books on a rigorous and gentle introduction to the foundations of mathematics for all users and learners of mathematics find, read. Almost everyone knows the game of tictactoe, in which players mark xs and os on a threebythree grid until one player makes three in a row, or the grid gets filled up with no winner a draw. Mathematical theories are expressed using first order logic. Set theory \a set is a many that allows itself to be thought of as a one. Introduction to logic and set theory 202014 general course notes december 2, 20 these notes were prepared as an aid to the student. Schwartz march 27, 2009 click here to view program.