An effective minimal encoding of uncountable sets
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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 W ⊆ ω 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].
Keywordsforcing minimal encoding relatively constructible set
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