Customer Reviews (4)

Definitive and Brilliant
This is still the definitive work on set theory and the continuum hypothesis. Although extremely terse, it is wonderfully clear and unburdened by the technical and pedantic details that doom many books in the subject. If you cannot track this down right now be patient, the American Mathematical Society is going to be reprinting it.

Professor Cohen passed away in March of 2007, but thankfully this book remains as a testament to his genius. Originally trained as an analyst, he began working on the continuum hypothesis knowing almost nothing about logic or set theory. Within two years he mastered the subject and solved the greatest outstanding problem in the field (and arguably in all of mathematics). Read this book if you want to understand one of the deepest ideas in all of human thought.

All-time classic -- a "desert island book"
Paul Cohen's "Set Theory and the Continuum Hypothesis" is not only the best technical treatment of his solution to the most notorious unsolved problem in mathematics, it is the best introduction to mathematical logic (though Manin's "A Course in Mathematical Logic" is also remarkably excellent and is the first book to read after this one).

Although it is only 154 pages, it is remarkably wide-ranging, and has held up very well in the 37 years since it was first published.Cohen is a very good mathematical writer and his arrangement of the material is irreproachable.All the arguments are well-motivated, the number of details left to the reader is not too large, and everything is set in a clear philosophical context. The book is completely self-contained and is rich with hints and ideas that will lead the reader to further work in mathematical logic.

It is one of my two favorite math books (the other being Conway's "On Numbers and Games").My copy is falling apart from extreme overuse.

A priceless gem
An "older" original work of a great mathematican.Not the best book to read about the subject, but certainly a collectors item.
I happen to have one because my master thesis used it as a major reference.It's the one book that everyone interested in the foundations of mathematics should own - if you can still get one.

Brilliant example of human greatness
This is one of the greatest math works ever. Prof. Cohen solves one of the most important problems in mathematics of this century, and this book explains his thinking and methods. A must for anyone who is reallyinterested in mathematics. ... Read more

Book Description

Kurt Gödel, mathematician and logician, was one of the most influential thinkers of the twentieth century. Gödel fled Nazi Germany, fearing for his Jewish wife and fed up with Nazi interference in the affairs of the mathematics institute at the University of Göttingen. In 1933 he settled at the Institute for Advanced Study in Princeton, where he joined the group of world-famous mathematicians who made up its original faculty.

His 1940 book, better known by its short title, The Consistency of the Continuum Hypothesis, is a classic of modern mathematics. The continuum hypothesis, introduced by mathematician George Cantor in 1877, states that there is no set of numbers between the integers and real numbers. It was later included as the first of mathematician David Hilbert's twenty-three unsolved math problems, famously delivered as a manifesto to the field of mathematics at the International Congress of Mathematicians in Paris in 1900. In The Consistency of the Continuum Hypothesis Gödel set forth his proof for this problem.

In 1999, Time magazine ranked him higher than fellow scientists Edwin Hubble, Enrico Fermi, John Maynard Keynes, James Watson, Francis Crick, and Jonas Salk. He is most renowned for his proof in 1931 of the 'incompleteness theorem,' in which he demonstrated that there are problems that cannot be solved by any set of rules or procedures. His proof wrought fruitful havoc in mathematics, logic, and beyond.

Book Description
This digital document is a journal article from Behaviour Research and Therapy, published by Elsevier in . The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.

Description:
Employing the autogenous-reactive model of obsessions (Behaviour Research and Therapy 41 (2003) 11-29), this study sought to test a hypothesized continuum where reactive obsessions fall in between autogenous obsessions and worry with respect to several thought characteristics concerning content appraisal, perceived form, and thought triggers. Nonclinical undergraduate students (n=435) were administered an online packet of questionnaires designed to examine the three different types of thoughts. Main data analyses included only those displaying moderate levels of obsessions or worries (n=252). According to the most distressing thought, three different groups were formed and compared: autogenous obsession (n=34), reactive obsession (n=76), and worry (n=142). Results revealed that (a) relative to worry, autogenous obsessions were perceived as more bizarre, more unacceptable, more unrealistic, and less likely to occur; (b) autogenous obsessions were more likely to take the form of impulses, urges, or images, whereas worry was more likely to take the form of doubts, apprehensions, or thoughts; and (c) worry was more characterized by awareness and identifiability of thought triggers, with reactive obsessions through these comparisons falling in between. Moreover, reactive obsessions, relative to autogenous obsessions, were more strongly associated with both severity of worry and use of worrying as a thought control strategy. Our data suggest that the reactive subtype represents more worry-like obsessions compared to the autogenous subtype. ... Read more

Book Description
Set Theory and the Continuum Problem is a novel introduction to set theory, including axiomatic development, consistency, and independence results. It is self-contained and covers all the set theory that a mathematician should know. Part I introduces set theory, including basic axioms,
development of the natural number system, Zorn's Lemma and other maximal principles. Part II proves the consistency of the continuum hypothesis and the axiom of choice, with material on collapsing mappings, model-theoretic results, and constructible sets. Part III presents a version of Cohen's
proofs of the independence of the continuum hypothesis and the axiom of choice.It also presents, for the first time in a textbook, the double inductionand superinduction principles, and Cowen's theorem. The book will interest students and researchers in logic and set theory. ... Read more

Customer Reviews (1)

Great book on set theory
I would imagine that introductory set theory books pose a significant problem for writers.Unless the reader has read a fair amount of mathematics, the material will seem unmotivated.On the other hand, if the reader has been exposed to mathematics, then she will find the introductory portion of the book boring and tedious.Smullyan & Fitting claimed to write an introductory book, but I don't think they did.

The introduction to sets is very fast.This is fine, as I fall into the class of people who find the introductions tedious.This is just a warning to anyone looking for a very introductory book: there are cheaper ones which you will understand better than this (Kamke, for example).

However, if you have had a fair amount of experience with logic and some set theory, then this book is great.The author's method of double induction brings together a large number of topics.Cohen's forcing method is presented with crystal clarity, and in a significantly interesting way.Independence proofs are, by their nature, generally tedious and pedantic.Yet the authors managed to make those presented very interesting.

Each chapter starts out with an interesting summary of the main ideas to be covered.This gives the reader a sort of "road map" in each chapter, allowing her to see where the chapter is headed, and how it is going to get there.This sort of thing is very important, but often lacking in mathematical books.

I highly recommend this book. ... Read more

Book Description
This digital document is a journal article from Behaviour Research and Therapy, published by Elsevier in . The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.

Description:
The objectives of the present study were to examine the degree of co-existence of hallucinations and delusions in the nonclinical population. In addition, we wished to investigate the role of metacognitions in hallucinations and delusions. Finally, we explored the relative roles of positive and negative metacognitive beliefs in proneness to hallucinations and delusions. Three hundred and thirty-one nonclinical participants completed instruments assessing: hallucination-proneness (Launay-Slade Hallucinations Scale; LSHS), delusion-proneness (21-item version of the Peters et al. Delusions Inventory; PDI-21) and metacognitive beliefs (Meta-Cognitions Questionnaire; MCQ). Participants were successively grouped according to their scores on the LSHS and the PDI-21. Results revealed that hallucination-proneness was positively and significantly associated with delusion-proneness. Furthermore, hallucination-prone and delusion-prone participants scored significantly higher on some sub-scales of the MCQ compared to non-prone participants. Finally, multiple regression analysis revealed that positive and negative beliefs were good predictors of proneness towards hallucinations and delusions. ... Read more

Product Description
The purpose of Cantor's theory is to distinguish between greater, and smaller infinities. To supply us with infinitely many infinities. But it turns out that Cantor's Theory has just one infinity.All the Cantorian infinities are equal to each other.All the distnict infinities, that are believed to be Cantorian, are Non-Cantorian.This tale is about these distinct infinities. ... Read more

Book Description
Since their appearance in the late 19th century, theCantor--Dedekind theory of real numbers and philosophy of thecontinuum have emerged as pillars of standard mathematical philosophy.On the other hand, this period also witnessed the emergence of avariety of alternative theories of real numbers and correspondingtheories of continua, as well as non-Archimedean geometry,non-standard analysis, and a number of important generalizations ofthe system of real numbers, some of which have been described asarithmetic continua of one type or another.
With the exception of E.W. Hobson's essay, which is concerned with theideas of Cantor and Dedekind and their reception at the turn of thecentury, the papers in the present collection are either concernedwith or are contributions to, the latter groups of studies. All thecontributors are outstanding authorities in their respective fields,and the essays, which are directed to historians and philosophers ofmathematics as well as to mathematicians who are concerned with thefoundations of their subject, are preceded by a lengthy historicalintroduction.
... Read more