Embedding of Countable Orders in Turing Degrees

被引：0

作者：

Sh. T. Ishmukhametov

机构：

[1] Ulyanovsk State University,

来源：

Mathematical Notes | 2002年 / 72卷

关键词：

recursive function; Turing degrees; embedding method; ordering; lattice;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In their classical papers, Lerman, Lachlan, and Lebeuf developed the embedding method, which provides constructions of initial segments of Turing degrees isomorphic to various partially ordered structures. We analyze this method and prove that there is a nonzero degree below each decreasing chain of degrees uniform in O'. This imposes restrictions on the application of the embedding method.

引用

页码：631 / 635

页数：4

共 8 条

[1]

Spector C.(1956)On degrees of recursive unsolvability Ann. of Math. 64 581-592

[2]

Shoenfield J. R.(1966)A theorem on minimal degrees J. Symbolic Logic 31 539-544

[3]

Titgemeyer D.(1962)Untersuchungen über die Struktur des Kleene-Postchen Halbverbandes des Grade der Rekursivenunl¨osbarkeit Arch. Math. Logik Grundlagenforsch 8 45-62

[4]

Hugill D. F.(1969)Initial segments of Turing degrees Proc. London Math. Soc. 19 1-16

[5]

Lerman M.(1969)Some nondistributive lattices as initial segments of the degrees of unsolvability J. Symbolic Logic 34 85-98

[6]

Lerman M.(1971)Initial segments of the degrees of unsolvability Ann. Math. 93 365-389

[7]

Lachlan A. H.(1976)Countable initial segments of the degrees of unsolvability J. Symbolic Logic 41 289-300

[8]

Lebeuf R.(undefined)undefined undefined undefined undefined-undefined

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