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Traditional logic as a part of philosophy is one of the oldest scientific disciplines. Mathematical logic, however, is a relatively young discipline and arose from the endeavors of Peano, Frege, Russell and others to create a logistic foundation for mathematics. It steadily developed during the 20th century into a broad discipline with several sub-areas and numerous applications in mathematics, informatics, linguistics and philosophy. While there are already several well-known textbooks on mathematical logic, this book is unique in that it is much more concise than most others, and the material is treated in a streamlined fashion which allows the professor to cover many important topics in a one semester course. Although the book is intended for use as a graduate text, the first three chapters could be understood by undergraduates interested in mathematical logic. These initial chapters cover just the material for an introductory course on mathematical logic combined with the necessary material from set theory. This material is of a descriptive nature, providing a view towards decision problems, automated theorem proving, non-standard models and other subjects. The remaining chapters contain material on logic programming for computer scientists, model theory, recursion theory, Godel's Incompleteness Theorems, and applications of mathematical logic. Philosophical and foundational problems of mathematics are discussed throughout the text. The author has provided exercises for each chapter, as well as hints to selected exercises. About the German edition: The book can be useful to the student and lecturer who prepares a mathematical logic course at the university. What a pity that the book is not written in a universal scientific language which mankind has not yet created. - A.Nabebin, Zentralblatt

Logic, Symbolic and mathematical --- Logic, Symbolic and mathematical.

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Logic, symbolic and mathematical --- Logic

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Devoted to the main areas of mathematical logic and applications to computer science, this volume features articles on weakly o-minimal theories, algorithmic complexity of relations, models within the computable model theory, hierarchies of randomness tests, computable numberings, and complexity problems of minimal unsatisfiable formulas.

Logic, Symbolic and mathematical --- Mathematics --- Math --- Science

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Isomorphisms (Mathematics). --- Isomorphisms (Mathematics) --- Logic, Symbolic and mathematical --- Logic, Symbolic and mathematical. --- Peano, Giuseppe,

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"Successfully addressing the frustration many students experience as they make the transition from computational mathematics to advanced calculus and algebraic structures, Theorems, Corollaries, Lemmas, and Methods of Proof equips students with the tools needed to succeed while providing a firm foundation in the axiomatic structure of modern mathematics. Intended as a main text for mathematics courses such as Methods of Proof, Transitions to Advanced Mathematics, and Foundations of Mathematics, the book may also be used as a supplementary textbook in junior- and senior-level courses on advanced calculus, real analysis, and modern algebra"--Jacket. This book: clearly explains the relationship between definitions, conjectures, theorems, corollaries, lemmas, and proofs; reinforces the foundations of calculus and algebra; explores how to use both a direct and indirect proof to prove a theorem; presents the basic properties of real numbers; discusses how to use mathematical induction to prove a theorem; identifies the different types of theorems; explains how to write a clear and understandable proof; and covers the basic structure of modern mathematics and the key components of modern mathematics.

Logic, Symbolic and mathematical --- 517.1 --- Proof theory --- Foundations