This is an ideal painless introduction to standard logic and set theory for anyone with a couple of years of undergraduate pure mathematics background. Symbolic logic does not figure significantly until the final chapter. An invaluable reference book for all mathematicians, this text is suitable for advanced undergraduates and graduate students. Numerous exercises make it particularly appropriate for classroom use. Synopsis Model theory deals with a branch of mathematical logic showing connections between a formal language and its interpretations or models. The treatmentalso contains much of interest toadvanced students in computerscience and philosophy. I essentially agree with what has been said.
Chapter 2 less elementary presents natural numbers, cardinal numbers, ordinal numbers, and the axiom of choice. Suitable for undergraduate and graduate courses, this book will also amuse and enlighten mathematically minded readers. The statement calculus, presented as a part of the predicate calculus, is treated in detail from the axiom schemes through the deduction theorem to the completeness theorem. Symbolizing sentences; logical inference; truth and validity; truth tables; terms, predicates, universal quantifiers; universal specification and laws of identity; more. Synopsis During the last two decades, methods that originated within mathematical logic have exhibited powerful applications to Banach space theory, particularly set theory and model theory.
Ideal for a one-semester course, this concise text offers more detail and mathematically relevant examples than those available in elementary books on logic. Then the metamathematical notions of consistency, completeness, independence, categoricity, and decidability are discussed, The predicate calculus is proved to be complete. Model theory deals with a branch of mathematical logic showing connections between a formal language and its interpretations or models. Jerome Keisler Number Of Pages 672 pages Series Dover Books on Mathematics Format Paperback Publication Date 2012-06-13 Language English Publisher Dover Publications, Incorporated Publication Year 2012 Additional Details Edition Number 3 Copyright Date 2012 Illustrated Yes Dimensions Weight 33. Carefully chosen exercises, with selected answers, help students test their grasp of the material. Mathematics, specifically the real number system, is approached as a unity whose operations can be logically ordered through axioms. Dover Publications Publication date Other books by C.
The real numbers are constructed here using Cauchy sequences rather than Dedekind cuts. Jerome Keisler Adult content: No Language: English Has Image Descriptions: No Categories: , , Submitted By: Bookshare Staff Usage Restrictions: This is a copyrighted book. Natural Number Sequence — Zorn's Lemma, etc. The final chapters present more advanced topics that feature a combination of several methods. Not too much is said about interpretations, but just enough to prepare the reader for later studying model theory if they are that way inclined.
Set Theory and Logic is the result of a course of lectures for advanced undergraduates, developed at Oberlin College for the purpose of introducing students to the conceptual foundations of mathematics. Finally Chapter 9 presents first-order languages and metamathematics, but not in too much depth. Suitable for advanced undergraduates and graduate students of mathematics, this exposition does not presuppose expertise in either model theory or Banach space theory. Chapter Three is devoted to first-order theories, i. Jerome Keisler, Mathematics Model Theory: Third Edition Dover Books on Mathematics Model theory deals with a branch of mathematical logic showing connections between a formal language and its interpretations or models. In Chapter Two, the predicate calculus is developed as a formal axiomatic theory.
The main theme of the book is mathematics as a system seen through the elaboration of real numbers; set theory and logic are seen s efficient tools in constructing axioms necessary to the system. For any student of mathematics, logic, or the interrelationship of the two, this book represents a thought-provoking introduction to the logical underpinnings of mathematical theory. Axioms and short developments are given for number theory and a few algebraic theories. Author Raymond Smullyan offers clear, incremental presentations of difficult logic concepts. One of the most complex and essential of modern mathematical innovations, the theory of sets crucial to quantum mechanics and other sciences , is introduced in a most careful concept manner, aiming for the maximum in clarity and stimulation for further study in set logic. Written in a light and witty style, Entertaining Mathematical Puzzles is a mixture of old and new riddles, grouped into sections that cover a variety of mathematical topics: money, speed, plane and solid geometry, probability, topology, tricky puzzles, and more.
Several key concepts are elaborated and there are plenty of proofs. This volume constitutes the first self-contained introduction to techniques of model theory in Banach space theory. Accessible to high school students, it also constitutes a valuable review of fundamentals for professionals. Additional topics include undecidability, combinatoric logic, and recursion theory. Puzzlists need only an elementary knowledge of math and a will to resist looking up the answer before trying to solve a problem. Role of the unconscious in invention; the medium of ideas — do they come to mind in words? Then the logic starts in Chapter 4 with basic propositional and predicate calculus.
Suitable for advanced undergraduates and graduate students of mathematics, this exposition does not presuppose expertise in either model theory or Banach space theory. This book is to be read and you can also see how the usefulness of the book Model Theory: Third Edition Dover Books on Mathematics. Its widespread influence extends to the author of Gödel, Escher, Bach, whose Pulitzer Prize—winning book was inspired by this work. Model Theory: Third Edition Dover Books on Mathematics by C. For instance, this volume offers a unified presentation of Krivine's theorem and the Krivine-Maurey theorem on stable Banach spaces, with emphasis on the connection between these results and basic model-theoretic notions such as types, indiscernible sequences, and ordinal ranks. The 1961 book was already very good, but this greatly expanded 1963 edition is much more comprehensive, and still very beginner-friendly, not one of those macho books which inflict the maximum pain on readers.