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Forcing Isomorphisms Between Dense Sets of Reals

Name: Forcing Isomorphisms Between Dense Sets of Reals
Brand: LAP Lambert Academic Publishing
SKU: 07137619
Price: 45.79 EUR
Availability: InStock
Author: Michael H. Vartanian
ISBN: 9783846528891

A Classic Result of Modern Set Theory

Michael H. Vartanian

Lingua

Inglese

Libro In brossura

Codice Libristo: 07137619

Casa editrice LAP Lambert Academic Publishing, novembre 2010

In founding set theory, Cantor showed that the cardinality of the set Q of rational numbers is count... Descrizione completa

Codice Libristo: 07137619

112 b

45.79 €

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In founding set theory, Cantor showed that the cardinality of the set Q of rational numbers is countably infinite; that Q may be extended by completion to obtain the set R of real numbers (we say that Q is countably dense in R); that any other countably dense subset of R is isomorphic to Q; and that R itself is uncountably infinite. The question then naturally arises whether all uncountably dense subsets of R of the same cardinality must also be isomorphic. Decades later, a negative answer was given when a model of set theory was constructed in which many uncountably dense subsets of R fail to be isomorphic. On the other hand, Baumgartner has shown by the method of forcing that another model exists in which all dense subsets of R of the least uncountable cardinality are isomorphic. Presented here is a detailed yet expository account of Baumgartner's famous result with a brief discussion of its relevance to forcing axioms in contemporary set theory.