The study of the degrees below 0' starts from Kleene and Post's seminalpaper [37]. Research in this area has led to the deep understanding ofTuring degrees and the development of various construction techniques.In many constructions, for example, in the construction of minimal degreesbelow 0', it is necessary to combine the priority argument with the sorts offorcing methods employed in the global theory. The difficulties encounteredin attempting to "localize" results from the global theory to degrees below0' have led to a better understanding of the nature of various constructions.
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