A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. Introduction to. Mathematical Logic. FOURTl-1 EI)ITJ()N. Elliott Mendelson. Queens College of the City University of New York. CHAPMAN & HALL. London· . A Mathematical Introduction to Logic by Herbert B. Enderton. Errata: If you have a recent printing, then some of these corrections might not apply to your copy.
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A Mathematical. Introduction to Logic. Second Edition. Herbert B. Enderton. University of California, Los Angeles. A Harcourt Science and Technology Company. A Mathematical Introduction to Logic: Herbert ronaldweinland.infoon and millions of other books are available for site Kindle. A Mathematical Introduction to Logic 2nd Edition. Start reading A Mathematical Introduction to Logic: Herbert ronaldweinland.infoon on your Kindle in under a minute. Sentential Logic. Informal Remarks on Formal Languages. The Language of Sentential Logic. Truth Assignments. A Parsing.
Each area has a distinct focus, although many techniques and results are shared among multiple areas. The borderlines amongst these fields, and the lines separating mathematical logic and other fields of mathematics, are not always sharp. The method of forcing is employed in set theory, model theory, and recursion theory, as well as in the study of intuitionistic mathematics. The mathematical field of category theory uses many formal axiomatic methods, and includes the study of categorical logic , but category theory is not ordinarily considered a subfield of mathematical logic. Because of its applicability in diverse fields of mathematics, mathematicians including Saunders Mac Lane have proposed category theory as a foundational system for mathematics, independent of set theory. These foundations use toposes , which resemble generalized models of set theory that may employ classical or nonclassical logic. The first half of the 20th century saw an explosion of fundamental results, accompanied by vigorous debate over the foundations of mathematics.
I thought abstract algebra was hard to follow but this book makes abstract algebra seem like a cakewalk.
The material is interesting but often confusing. Definitions seem to contradict each other because of the way things are worded so similarly. This book is TOO formal which makes conceptualizing theorems impossible. Often times, notations are used without explanation. If you are a beginner, avoid this book at all cost. If you're an expert, then you might like it. The reason I am giving this a one star is because it is no "introduction". This is a great book as far as content goes.
I would give the book five stars if it wasn't for the poor binding these books seem to have. I downloadd this book for a course in logic. When I cracked it open the first time, the binding from the spine of the book began to separate from the cover along with the paper holding it in.
I am not the only person experiencing this problem as well. Of two friends of mine in the course, similar issues have happened. FIRST : As I reached half the book it was already giving signs of a strong "desire" to fall apart, with the front pages almost ripped off and the next pages soon to follow THIRD : A very peculiar way of proving theorems : quite a personal interpretation of induction and recursion a way for Enderton to free himself from the burden of really getting at the bottom of things It seems like Enderton had enrolled in a marathonian effort to give tortuous proofs, often incomplete and based on fistulous definitions, which turn the reading into a continual second-guessing exercise, with its load of annotations Added to the annoying game of transferring part of the theory to a bunch of exercises.
And was disappointed. This is easily the BEST intro.
Yes, I sound horribly biased. It's the only MATH book on logic out there that is easy to understand and yet formal enough to be considered "mathematical. Truth and models the heart of it are treated incredibly clearly. Extra topics such as interpretations between theories and nonstandard analysis keep things exciting for a math book.
His treatment of undecidability is well-written and lucid.
The second order stuff is fun. I loved this book. As far as math teachers go, Enderton is top notch. Even someone as unacquainted with math as I was when I studied the book and as I still am now, I guess understood what was going on.
To be honest though, I did have one advantage, I was a student of the master, Enderton, himself.
I learned so much about logic and math in general from this great book. I was fortunate enough to study some more with Enderton throughout my years as a student. Herbert B. Be the first to write a review. Add to Wishlist. Ships in 15 business days. Description Table of Contents Product Details Click on the cover image above to read some pages of this book! Preface p. All Rights Reserved.
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The success in axiomatizing geometry motivated Hilbert to seek complete axiomatizations of other areas of mathematics, such as the natural numbers and the real line. This would prove to be a major area of research in the first half of the 20th century. The 19th century saw great advances in the theory of real analysis , including theories of convergence of functions and Fourier series.
Mathematicians such as Karl Weierstrass began to construct functions that stretched intuition, such as nowhere-differentiable continuous functions. Previous conceptions of a function as a rule for computation, or a smooth graph, were no longer adequate.
Weierstrass began to advocate the arithmetization of analysis , which sought to axiomatize analysis using properties of the natural numbers. Cauchy in defined continuity in terms of infinitesimals see Cours d'Analyse, page In , Dedekind proposed a definition of the real numbers in terms of Dedekind cuts of rational numbers Dedekind , a definition still employed in contemporary texts. Georg Cantor developed the fundamental concepts of infinite set theory.
His early results developed the theory of cardinality and proved that the reals and the natural numbers have different cardinalities Cantor Over the next twenty years, Cantor developed a theory of transfinite numbers in a series of publications. In , he published a new proof of the uncountability of the real numbers that introduced the diagonal argument , and used this method to prove Cantor's theorem that no set can have the same cardinality as its powerset.
Cantor believed that every set could be well-ordered , but was unable to produce a proof for this result, leaving it as an open problem in Katz , p. The discovery of paradoxes in informal set theory caused some to wonder whether mathematics itself is inconsistent, and to look for proofs of consistency.
In , Hilbert posed a famous list of 23 problems for the next century. The first two of these were to resolve the continuum hypothesis and prove the consistency of elementary arithmetic, respectively; the tenth was to produce a method that could decide whether a multivariate polynomial equation over the integers has a solution.
Subsequent work to resolve these problems shaped the direction of mathematical logic, as did the effort to resolve Hilbert's Entscheidungsproblem , posed in This problem asked for a procedure that would decide, given a formalized mathematical statement, whether the statement is true or false.
Set theory and paradoxes[ edit ] Ernst Zermelo gave a proof that every set could be well-ordered, a result Georg Cantor had been unable to obtain. To achieve the proof, Zermelo introduced the axiom of choice , which drew heated debate and research among mathematicians and the pioneers of set theory. The immediate criticism of the method led Zermelo to publish a second exposition of his result, directly addressing criticisms of his proof Zermelo a.
This paper led to the general acceptance of the axiom of choice in the mathematics community. Skepticism about the axiom of choice was reinforced by recently discovered paradoxes in naive set theory. Cesare Burali-Forti was the first to state a paradox: the Burali-Forti paradox shows that the collection of all ordinal numbers cannot form a set.