Forcing Isomorphisms Between Dense Sets of Reals

Name: Forcing Isomorphisms Between Dense Sets of Reals
Brand: LAP Lambert Academic Publishing
SKU: 9783846528891
Price: 184.07 PLN
Availability: InStock

A Classic Result of Modern Set Theory

Autor: Michael H. Vartanian

Język:

Oprawa: Miękka

Wydawca: LAP Lambert Academic Publishing

Dostępność: Dostępna u dostawcy

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

Informacje o książce

Autor

Michael H. Vartanian

Język

Angielski

Oprawa

Książka - Miękka

Data wydania

2011

strony

EAN

9783846528891

Enbook ID

07137619

Wydawca

LAP Lambert Academic Publishing

Waga

100

Wymiary

150 x 220 x 3

Pełny opis

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.

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Forcing Isomorphisms Between Dense Sets of Reals

A Classic Result of Modern Set Theory

Informacje o książce

Pełny opis

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