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Upper Bounds on Locally Countable Admissible Initial Segments of a Turing Degree Hierarchy
Hodes, Harold T.
J. Symbolic Logic, Tome 46 (1981) no. 1, p. 753-760 / Harvested from Project Euclid
Where AR is the set of arithmetic Turing degrees, 0^{(\omega}) is the least member of {\mathbf{\alpha}^{(2)} |\mathbf{a} is an upper bound on \mathrm{AR}}. This situation is quite different if we examine HYP, the set of hyperarithmetic degrees. We shall prove (Corollary 1) that there is an a, an upper bound on \mathbf{HYP}, whose hyperjump is the degree of Kleene's \mathcal{O}. This paper generalizes this example, using an iteration of the jump operation into the transfinite which is based on results of Jensen and is detailed in [3] and [4]. In \S1 we review the basic definitions from [3] which are needed to state the general results.
Publié le : 1981-12-14
Classification: 
@article{1183740885,
     author = {Hodes, Harold T.},
     title = {Upper Bounds on Locally Countable Admissible Initial Segments of a Turing Degree Hierarchy},
     journal = {J. Symbolic Logic},
     volume = {46},
     number = {1},
     year = {1981},
     pages = { 753-760},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183740885}
}
Hodes, Harold T. Upper Bounds on Locally Countable Admissible Initial Segments of a Turing Degree Hierarchy. J. Symbolic Logic, Tome 46 (1981) no. 1, pp.  753-760. http://gdmltest.u-ga.fr/item/1183740885/