On the subject of stomach and gastric diseases, current clinical, morphological, pharmacological, biochemical as well as cellular and molecularbiological aspects will be presented. The articles of the first part of this book will discuss the normal functions of the stomach (such as motility, secretion, tissue regeneration etc.). The second part deals with pathophysiological aspects (such as inflammation, ulceration and tumor formation) and modern possibilities of treatment. The authors aim at gaining a deeper knowledge of the stomach, its physiology and pathophysiology in order to use this knowledge for the better of their patients.

Finite Model Theory: Second Edition (Springer Monographs in Mathematics)

Computers & Technology

Ebbinghaus, Heinz-Dieter

Flum, Jörg

Computer Science

Springer

This book is about all kinds of numbers, from rationals to octonians, reals to infinitesimals. It is a story about a major thread of mathematics over thousands of years, and it answers everything from why Hamilton was obsessed with quaternions to what the prospect was for quaternionic analysis in the 19th century. It glimpses the mystery surrounding imaginary numbers in the 17th century and views some major developments of the 20th century.

Numbers (Graduate Texts in Mathematics, 123)

Science & Math

Mathematics

This is a book about numbers - all kinds of numbers, from integers to "p"-adics, from rationals to octonions, from reals to infinitesimals. Who first used the standard notation for A, ? Why was Hamilton obsessed with quaternions? What was the prospect for "quaternionic analysis" in the 19th century? This is the story about one of the major threads of mathematics over thousands of years. It is a story that will give the reader both a glimpse of the mystery surrounding imaginary numbers in the 17th century and also a view of some major developments in the 20th.

Numbers

Mathematical Logic (Graduate Texts in Mathematics)

Product Description 
This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming. 
 From the Back Cover 
This textbook introduces first-order logic and its role in the foundations of mathematics by examining fundamental questions. What is a mathematical proof? How can mathematical proofs be justified? Are there limitations to provability? To what extent can machines carry out mathematical proofs? In answering these questions, this textbook explores the capabilities and limitations of algorithms and proof methods in mathematics and computer science. 
The chapters are carefully organized, featuring complete proofs and numerous examples throughout. Beginning with motivating examples, the book goes on to present the syntax and semantics of first-order logic. After providing a sequent calculus for this logic, a Henkin-type proof of the completeness theorem is given. These introductory chapters prepare the reader for the advanced topics that follow, such as Gödel's Incompleteness Theorems, Trakhtenbrot's undecidability theorem, Lindström's theorems on the maximality of first-order logic, and results linking logic with automata theory. This new edition features many modernizations, as well as two additional important results: The decidability of Presburger arithmetic, and the decidability of the weak monadic theory of the successor function. 
Mathematical Logic is ideal for students beginning their studies in logic and the foundations of mathematics. Although the primary audience for this textbook will be graduate students or advanced undergraduates in mathematics or computer science, in fact the book has few formal prerequisites. It demands of the reader only mathematical maturity and experience with basic abstract structures, such as those encountered in discrete mathematics or algebra. 
 About the Author 
Heinz-Dieter Ebbinghaus is Professor Emeritus at the Mathematical Institute of the University of Freiburg. His work spans fields in logic, such as model theory and set theory, and includes historical aspects. 
Jörg Flum is Professor Emeritus at the Mathematical Institute of the University of Freiburg. His research interests include mathematical logic, finite model theory, and parameterized complexity theory. 
Wolfgang Thomas is Professor Emeritus at the Computer Science Department of RWTH Aachen University. His research interests focus on logic in computer science, in particular logical aspects of automata theory.

Mathematical Logic (Graduate Texts in Mathematics, 291)

Thomas, Wolfgang

This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.

This is a thoroughly revised and enlarged second edition that presents the main results of descriptive complexity theory, that is, the connections between axiomatizability of classes of finite structures and their complexity with respect to time and space bounds. The logics that are important in this context include fixed-point logics, transitive closure logics, and also certain infinitary languages; their model theory is studied in full detail. The book is written in such a way that the respective parts on model theory and descriptive complexity theory may be read independently.

Mathematik zu erlernen und zu lehren gilt als schwierig. Die Begriffe reelle und komplexe Zahlen oder die Kreiszahl Pi sind zwar vielen bekannt, aber nur wenige wissen, was dahinter steckt. Leser, die erfahren wollen, was sich wirklich dahinter verbirgt, werden in diesem Band an die Magie der Mathematik herangeführt: „Das Lesen ist ein Genuß, den man sich nicht entgehen lassen sollte." (Jahresbericht der Deutschen Mathematiker-Vereinigung).

Zahlen (Springer-Lehrbuch) (German Edition)

Finite model theory has its origin in classical model theory, but owes its systematic development to research from complexity theory. The book presents the main results of descriptive complexity theory, that is, the connections between axiomatizability of classes of finite structures and their complexity with respect to time and space bounds. The logics that are important in this context include fixed- point logics, transitive closure logics, and also certain infinitary languages; their model theory is studied in full detail. Other topics include DATALOG languages, quantifiers and oracles, 0-1 laws, and optimization and approximation problems. The book is written in such a way that the resp. parts on model theory and descriptive complexity theory may be read independently.

Finite Model Theory (Perspectives in Mathematical Logic)

Finite Model Theory

This junior/senior level text is devoted to a study of first-order logic and its role in the foundations of mathematics: What is a proof? How can a proof be justified? To what extent can a proof be made a purely mechanical procedure? How much faith can we have in a proof that is so complex that no one can follow it through in a lifetime? The first substantial answers to these questions have only been obtained in this century. The most striking results are contained in Goedells work: First, it is possible to give a simple set of rules that suffice to carry out all mathematical proofs; but, second, these rules are necessarily incomplete - it is impossible, for example, to prove all true statements of arithmetic. The book begins with an introduction to first-order logic, Goedel's theorem, and model theory. A second part covers extensions of first-order logic and limitations of the formal methods. The book covers several advanced topics, not commonly treated in introductory texts, such as Trachtenbrot's undecidability theorem. Fraisse's elementary equivalence, and Lindstroem's theorem on the maximality of first-order logic.

Mathematical logic (Undergraduate texts in mathematics)

Springer, Verlag

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Books by Ebbinghaus, Heinz-Dieter

See the best price to sell, buy, or rent books by Ebbinghaus, Heinz-Dieter. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Finite Model Theory: Second Edition (Springer Monographs in Mathematics)

Numbers (Graduate Texts in Mathematics, 123)

Numbers

Mathematical Logic (Graduate Texts in Mathematics, 291)

Mathematical Logic (Graduate Texts in Mathematics)

Finite Model Theory: Second Edition (Springer Monographs in Mathematics)

Zahlen (Springer-Lehrbuch) (German Edition)

Finite Model Theory (Perspectives in Mathematical Logic)

Finite Model Theory

Mathematical logic (Undergraduate texts in mathematics)