The foundations of mathematics include mathematical logic, set theory, recursion theory, model theory, and Gödel's incompleteness theorems. Professor Wolf provides here a guide that any interested reader with some post-calculus experience in mathematics can read, enjoy, and learn from. It could also serve as a textbook for courses in the foundations of mathematics, at the undergraduate or graduate level. The book is deliberately less structured and more user-friendly than standard texts on foundations, so will also be attractive to those outside the classroom environment wanting to learn about the subject.
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Editorial Reviews
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An enjoyable account that hits the highlights while omitting the messy details. -- Martin Davis
Book Description
Professor Wolf provides a guide that any interested reader with some post-calculus experience in mathematics can read, enjoy, and learn from. Covering the foundations of mathematics, it is more user-friendly than standard texts so will also be attractive to those outside the classroom environment.
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5.0 out of 5 stars
An in-depth and in-breadth tour of the foundations of mathematics,
By Charles Ashbacher (Marion, Iowa United States) - See all my reviews (TOP 500 REVIEWER) (VINE VOICE) (HALL OF FAME REVIEWER)
This review is from: A Tour Through Mathematical Logic (Carus Mathematical Monographs) (Paperback)
This tour is both broad and deep; it covers most of what would ordinarily be considered upper level material in the foundations of mathematics. While it contains theorems, proofs and exercises, it does not have the structure of a textbook. It is more on the order of an advanced survey that includes history. There are occasional short sections reserved for biographies of mathematicians of note in the field. For example, there are biographies of Bertrand Russell, Euclid, Georg Cantor, John von Neumann and Julia Robinson.The chapter headings are: *) Predicate logic *) Axiomatic set theory *) Recursion theory and computability *) Godel's incompleteness theorems *) Model theory *) Contemporary set theory *) Nonstandard analysis *) Constructive mathematics Given the branching away from logic into set theory and analysis, in my opinion, this book is best considered a survey of the foundations of mathematics. Considered in that way, it is a sound primer for people with mathematical maturity. If you have an interest in advanced material in these areas, you will find this book worthy of study.
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Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Inside This Book
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First Sentence:
The basic principles of logic and its use in mathematics were well understood by the philosophers and mathematicians of the classical Greek era, and Aristotle provided the first systematic written treatment of logic (propositional logic, primarily). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
propositional consequence, proper axioms, formalist program, inverse axiom, transitive model, dense ordering, derivability conditions, regularity axiom, prenex formula, transitive class, commutative ring with unity, large cardinal axioms, limit cardinal, large cardinals, cumulative hierarchy, partial recursive functions, ordinary mathematics, recursion theorem, see the next exercise, first incompleteness theorem, cardinal arithmetic, constructive mathematics, denumerable number, measurable cardinals, axiom schema Key Phrases - Capitalized Phrases (CAPs): (learn more)
Julia Robinson, King's College, Leonhard Euler, Principia Mathematica New!
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Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
The basic principles of logic and its use in mathematics were well understood by the philosophers and mathematicians of the classical Greek era, and Aristotle provided the first systematic written treatment of logic (propositional logic, primarily). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
propositional consequence, proper axioms, formalist program, inverse axiom, transitive model, dense ordering, derivability conditions, regularity axiom, prenex formula, transitive class, commutative ring with unity, large cardinal axioms, limit cardinal, large cardinals, cumulative hierarchy, partial recursive functions, ordinary mathematics, recursion theorem, see the next exercise, first incompleteness theorem, cardinal arithmetic, constructive mathematics, denumerable number, measurable cardinals, axiom schema Key Phrases - Capitalized Phrases (CAPs): (learn more)
Julia Robinson, King's College, Leonhard Euler, Principia Mathematica New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Citations (learn more)
This book cites 76
books:
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- Model Theory, Third Edition (Studies in Logic and the Foundations of Mathematics) by C.C. Chang in Back Matter (1), and Back Matter (2)
- Constructive Analysis (Grundlehren Der Mathematischen Wissenschaften) by Errett Bishop on page 330, and Back Matter
- A History of Western Philosophy by Bertrand Russell on page 6
- An Introduction to the History of Mathematics (Saunders Series) by Howard Eves in Back Matter
- Discrete Mathematics by Wiley in Back Matter
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