Elements of Mathematical Logic and Set Theory
Author | : Jerzy Słupecki |
Publisher | : Pergamon |
Total Pages | : 374 |
Release | : 1967 |
Genre | : Mathematics |
ISBN | : |
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Author | : Jerzy Słupecki |
Publisher | : Pergamon |
Total Pages | : 374 |
Release | : 1967 |
Genre | : Mathematics |
ISBN | : |
Author | : Jerzy Słupecki |
Publisher | : Pergamon |
Total Pages | : 372 |
Release | : 1967 |
Genre | : Mathematics |
ISBN | : |
Author | : Herbert B. Enderton |
Publisher | : Academic Press |
Total Pages | : 279 |
Release | : 1977-05-23 |
Genre | : Mathematics |
ISBN | : 0080570429 |
This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.
Author | : Paul C. Rosenbloom |
Publisher | : |
Total Pages | : 234 |
Release | : 1950 |
Genre | : Logic, Symbolic and mathematical |
ISBN | : |
"This book is intended for readers who, while mature mathematically, have no knowledge of mathematical logic. We attempt to introduce the reader to the most important approaches to the subject, and, wherever possible within the limitations of space which we have set for ourselves, to give at least a few nontrivial results illustrating each of the important methods for attacking logical problems"--Preface.
Author | : Robert R. Stoll |
Publisher | : Courier Corporation |
Total Pages | : 512 |
Release | : 2012-05-23 |
Genre | : Mathematics |
ISBN | : 0486139646 |
Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories.
Author | : D.L. Johnson |
Publisher | : Springer Science & Business Media |
Total Pages | : 179 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1447106032 |
In mathematics we are interested in why a particular formula is true. Intuition and statistical evidence are insufficient, so we need to construct a formal logical proof. The purpose of this book is to describe why such proofs are important, what they are made of, how to recognize valid ones, how to distinguish different kinds, and how to construct them. This book is written for 1st year students with no previous experience of formulating proofs. Dave Johnson has drawn from his considerable experience to provide a text that concentrates on the most important elements of the subject using clear, simple explanations that require no background knowledge of logic. It gives many useful examples and problems, many with fully-worked solutions at the end of the book. In addition to a comprehensive index, there is also a useful `Dramatis Personae` an index to the many symbols introduced in the text, most of which will be new to students and which will be used throughout their degree programme.
Author | : Peter G. Hinman |
Publisher | : CRC Press |
Total Pages | : 894 |
Release | : 2018-10-08 |
Genre | : Mathematics |
ISBN | : 1439864276 |
This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Gödel's Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory. Based on the author's more than 35 years of teaching experience, the book develops students' intuition by presenting complex ideas in the simplest context for which they make sense. The book is appropriate for use as a classroom text, for self-study, and as a reference on the state of modern logic.
Author | : Jerome Malitz |
Publisher | : Springer Science & Business Media |
Total Pages | : 209 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461394414 |
This book is intended as an undergraduate senior level or beginning graduate level text for mathematical logic. There are virtually no prere quisites, although a familiarity with notions encountered in a beginning course in abstract algebra such as groups, rings, and fields will be useful in providing some motivation for the topics in Part III. An attempt has been made to develop the beginning of each part slowly and then to gradually quicken the pace and the complexity of the material. Each part ends with a brief introduction to selected topics of current interest. The text is divided into three parts: one dealing with set theory, another with computable function theory, and the last with model theory. Part III relies heavily on the notation, concepts and results discussed in Part I and to some extent on Part II. Parts I and II are independent of each other, and each provides enough material for a one semester course. The exercises cover a wide range of difficulty with an emphasis on more routine problems in the earlier sections of each part in order to familiarize the reader with the new notions and methods. The more difficult exercises are accompanied by hints. In some cases significant theorems are devel oped step by step with hints in the problems. Such theorems are not used later in the sequence.
Author | : Michael L. O'Leary |
Publisher | : John Wiley & Sons |
Total Pages | : 464 |
Release | : 2015-09-14 |
Genre | : Mathematics |
ISBN | : 1118548019 |
A mathematical introduction to the theory and applications of logic and set theory with an emphasis on writing proofs 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 complex problems. The book begins with propositional logic, including two-column proofs and truth table applications, followed by first-order logic, which provides the structure for writing mathematical proofs. Set theory is then introduced and serves as the basis for defining relations, functions, numbers, mathematical induction, ordinals, and cardinals. The book concludes with a primer on basic model theory with applications to abstract algebra. A First Course in Mathematical Logic and Set Theory also includes: Section exercises designed to show the interactions between topics and reinforce the presented ideas and concepts Numerous examples that illustrate theorems and employ basic concepts such as Euclid’s lemma, the Fibonacci sequence, and unique factorization Coverage of important theorems including the well-ordering theorem, completeness theorem, compactness theorem, as well as the theorems of Löwenheim–Skolem, Burali-Forti, Hartogs, Cantor–Schröder–Bernstein, and König An excellent textbook for students studying the foundations of mathematics and mathematical proofs, A First Course in Mathematical Logic and Set Theory is also appropriate for readers preparing for careers in mathematics education or computer science. In addition, the book is ideal for introductory courses on mathematical logic and/or set theory and appropriate for upper-undergraduate transition courses with rigorous mathematical reasoning involving algebra, number theory, or analysis.
Author | : Douglas Cenzer |
Publisher | : World Scientific |
Total Pages | : 222 |
Release | : 2020-04-04 |
Genre | : Mathematics |
ISBN | : 9811201943 |
This book provides an introduction to axiomatic set theory and descriptive set theory. 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.The book is designed as a flexible and accessible text for a one-semester introductory course in set theory, where the existing alternatives may be more demanding or specialized. Readers will learn the universally accepted basis of the field, with several popular topics added as an option. Pointers to more advanced study are scattered throughout the text.