Mathematical Logic

On Numbers, Sets, Structures, and Symmetry

Nonfiction, Science & Nature, Mathematics, Logic, History
Cover of the book Mathematical Logic by Roman Kossak, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Roman Kossak ISBN: 9783319972985
Publisher: Springer International Publishing Publication: October 3, 2018
Imprint: Springer Language: English
Author: Roman Kossak
ISBN: 9783319972985
Publisher: Springer International Publishing
Publication: October 3, 2018
Imprint: Springer
Language: English

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. 

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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. 

More books from Springer International Publishing

Cover of the book Modern Methods in Collisional-Radiative Modeling of Plasmas by Roman Kossak
Cover of the book Innovations in the Treatment of Substance Addiction by Roman Kossak
Cover of the book Non-commutative Multiple-Valued Logic Algebras by Roman Kossak
Cover of the book Internet of Things. User-Centric IoT by Roman Kossak
Cover of the book Phenomenology and Intercultural Understanding by Roman Kossak
Cover of the book Myxozoan Evolution, Ecology and Development by Roman Kossak
Cover of the book Information Security and Privacy by Roman Kossak
Cover of the book Computer Security – ESORICS 2017 by Roman Kossak
Cover of the book Exotic Nuclear Excitations: The Transverse Wobbling Mode in 135 Pr by Roman Kossak
Cover of the book Thermodynamic Properties of Cryogenic Fluids by Roman Kossak
Cover of the book Neuroimaging Pharmacopoeia by Roman Kossak
Cover of the book Shale Analytics by Roman Kossak
Cover of the book Endogenous ADP-Ribosylation by Roman Kossak
Cover of the book Aristotle’s Practical Philosophy by Roman Kossak
Cover of the book Design and Analysis of Simulation Experiments by Roman Kossak
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy