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Definability and initial segments of c-degrees

  • Robert S. Lubarsky (a1)


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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[G]Groszek, Marcia, in preparation.
[J]Jensen, Ronald, Definable sets of minimal degree, Mathematical logic and foundations of set theory (Bar-Hillel, Y., editor), North-Holland, Amsterdam, 1970, pp. 122128.
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[Lu]Lubarsky, Robert, Lattices of c-degrees, Annals of Pure and Applied Logic, vol. 36 (1987), pp. 115118.
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