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The Consistency of the Axion of Choice and of the Generalized Continuum Hypothesis with the Axioms of Set Theory (Annals of Mathematics Studies, No. 3)
 
 
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The Consistency of the Axion of Choice and of the Generalized Continuum Hypothesis with the Axioms of Set Theory (Annals of Mathematics Studies, No. 3) [Paperback]

Kurt Gödel (Author)

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Book Description

September 1, 1940 0691079277 978-0691079271

Kurt Gdel, mathematician and logician, was one of the most influential thinkers of the twentieth century. Gdel 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 Gttingen. 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 Gdel 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.


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Inside This Book (learn more)
First Sentence:
Our primitive notions are: class, denoted by ; set, denoted by ; and the diadic relation between class and class, class and set, set and class, or set and set. Read the first page
Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
normal propositional function, constructible classes, isomorphism with respect, defining postulate, constructible set, propositional functions, proper class
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