Some recent developments in higher recursion theory

Journal of Symbolic Logic 48 (3):629-642 (1983)
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Abstract

In recent years higher recursion theory has experienced a deep interaction with other areas of logic, particularly set theory (fine structure, forcing, and combinatorics) and infinitary model theory. In this paper we wish to illustrate this interaction by surveying the progress that has been made in two areas: the global theory of the κ-degrees and the study of closure ordinals

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10.2307/2273455

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Citations of this work

Applications of Fodor's lemma to Vaught's conjecture.Mark Howard - 1989 - Annals of Pure and Applied Logic 42 (1):1-19.
Incomparable Vγ$V_\gamma$‐degrees.Teng Zhang - 2023 - Mathematical Logic Quarterly 69 (1):58-62.

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References found in this work

The fine structure of the constructible hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.
Perfect-set forcing for uncountable cardinals.Akihiro Kanamori - 1980 - Annals of Mathematical Logic 19 (1-2):97-114.
Some applications of Jensen's coding theorem.R. David - 1982 - Annals of Mathematical Logic 22 (2):177-196.
Steel forcing and barwise compactness.Sy D. Friedman - 1982 - Annals of Mathematical Logic 22 (1):31-46.
Scott sentences and admissible sets.Mark Nadel - 1974 - Annals of Mathematical Logic 7 (2):267.

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