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Siberian Mathematical Journal

, 52:854 | Cite as

An effective minimal encoding of uncountable sets

  • V. G. Kanovei
  • V. A. Lyubetsky
Article

Abstract

We propose a method for encoding sets of the countable ordinals by generic reals which preserves cardinality and enjoys the property of minimality over the encoded set.

For Wω 1 there is a cardinal-preserving generic extension L[W][x] of the class L[W] by a generic real x such that W belongs to the class L[x], i.e., W is Gödel constructible with respect to x, while x itself is minimal over L[W].

Keywords

forcing minimal encoding relatively constructible set 

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Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.Kharkevich Institute for Information Transmission ProblemsMoscowRussia

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