Elements Of Mathematical Logic
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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 | : Jerzy Słupecki |
Publisher | : Pergamon |
Total Pages | : 374 |
Release | : 1967 |
Genre | : Mathematics |
ISBN | : |
Author | : Georg Kreisel |
Publisher | : Elsevier |
Total Pages | : 222 |
Release | : 1967 |
Genre | : Electronic books |
ISBN | : 9780444534125 |
Author | : Jan Łukasiewicz |
Publisher | : |
Total Pages | : 127 |
Release | : 1966 |
Genre | : Logic, Symbolic and mathematical |
ISBN | : |
Author | : Roman Kossak |
Publisher | : Springer |
Total Pages | : 188 |
Release | : 2018-10-03 |
Genre | : Mathematics |
ISBN | : 3319972987 |
This book, presented in two parts, offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions. Its first part, Logic Sets, and Numbers, shows how mathematical logic is used to develop the number structures of classical mathematics. The exposition does not assume any prerequisites; it is rigorous, but as informal as possible. All necessary concepts are introduced exactly as they would be in a course in mathematical logic; but are accompanied by more extensive introductory remarks and examples to motivate formal developments. The second part, Relations, Structures, Geometry, introduces several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions, and shows how they are used to study and classify mathematical structures. Although more advanced, this second part is accessible to the reader who is either already familiar with basic mathematical logic, or has carefully read the first part of the book. Classical developments in model theory, including the Compactness Theorem and its uses, are discussed. Other topics include tameness, minimality, and order minimality of structures. The book can be used as an introduction to model theory, but unlike standard texts, it does not require familiarity with abstract algebra. This book will also be of interest to mathematicians who know the technical aspects of the subject, but are not familiar with its history and philosophical background.
Author | : Wolfgang Rautenberg |
Publisher | : Springer |
Total Pages | : 337 |
Release | : 2010-07-01 |
Genre | : Mathematics |
ISBN | : 1441912215 |
Mathematical logic developed into a broad discipline with many applications in mathematics, informatics, linguistics and philosophy. This text introduces the fundamentals of this field, and this new edition has been thoroughly expanded and revised.
Author | : Jerzy Słupecki |
Publisher | : Pergamon |
Total Pages | : 374 |
Release | : 1967 |
Genre | : Mathematics |
ISBN | : |
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 | : Jan Lukasiewicz |
Publisher | : |
Total Pages | : 127 |
Release | : 1991 |
Genre | : |
ISBN | : |
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.