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Definability and initial segments of c-degrees
Published online by Cambridge University Press: 12 March 2014
Abstract
We combine two techniques of set theory relating to mininal degrees of constructibility. Jensen constructed a minimal real which is additionally a singleton. Groszek built an initial segment of order type 1 + α*, for any ordinal α. This paper shows how to force a
singleton such that the c-degrees beneath it, all represented by reals, are of type 1 + α*, for many ordinals α. We also examine the definability α needs to be so represented by a real.
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- Copyright © Association for Symbolic Logic 1988