On coding uncountable sets by reals
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Joan Bagaria; Vladimir Kanovei
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Article
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2010
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John Wiley and Sons
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English
โ 273 KB
## Abstract If __A__ โ ฯ~1~, then there exists a cardinal preserving generic extension ๐[__A__ ][__x__ ] of ๐[__A__ ] by a real __x__ such that 1) __A__ โ ๐[__x__ ] and __A__ is ฮ~1~^HC^ (__x__) in ๐[__x__ ]; 2) __x__ is minimal over ๐[__A__ ], that is, if a set __Y__ belongs to ๐[__x__ ], then e