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- W130660187 abstract "The unresolved character of the power set operation stymies the solution of elementary problems arising in Kleene's theory of recursion in objects of finite type. E.g. Post's problem for 3E has a positive solution if V=L (NORMANN, 1975), and a negative if AD holds. Let δ be the class of all sets R ⊆ 2ω such that R is recursive in 3E, b for some real b. A forcing construction shows δ is not recursively enumerable in 3E when there is a recursively regular well-ordering of 2″ recursive in 3E. It follows that the concepts of Σ*, and weak Σ*, definability differ. With the aid of the notions of indexicality and ordinal recursiveness, an absolute version of Post's problem for 3E is devised, and studied when certain recursively enumerable projecta are equal." @default.
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- W130660187 date "1980-01-01" @default.
- W130660187 modified "2023-10-15" @default.
- W130660187 title "Post's Problem, Absoluteness and Recursion in Finite Types" @default.
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- W130660187 doi "https://doi.org/10.1016/s0049-237x(08)71261-8" @default.
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