Embedding lattices in the Kleene degrees
Muraki, Hisato
Fundamenta Mathematicae, Tome 159 (1999), p. 47-64 / Harvested from The Polish Digital Mathematics Library
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Under ZFC+CH, we prove that some lattices whose cardinalities do not exceed ℵ1 can be embedded in some local structures of Kleene degrees.

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:212412 
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     title = {Embedding lattices in the Kleene degrees},
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     volume = {159},
     year = {1999},
     pages = {47-64},
     zbl = {0947.03062},
     language = {en},
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Muraki, Hisato. Embedding lattices in the Kleene degrees. Fundamenta Mathematicae, Tome 159 (1999) pp. 47-64. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv162i1p47bwm/

[00000] [1] K. J. Devlin, Constructibility, Springer, 1984.

[00001] [2] K. Hrbáček, On the complexity of analytic sets, Z. Math. Logik Grundlag. Math. 24 (1978), 419-425. | Zbl 0411.03040

[00002] [3] M. Lerman, Degrees of Unsolvability, Springer, 1983.

[00003] [4] H. Muraki, Local density of Kleene degrees, Math. Logic Quart. 43 (1995), 183-189. | Zbl 0820.03030

[00004] [5] H. Muraki, Non-distributive upper semilattice of Kleene degrees, J. Symbolic Logic 64 (1999), 147-158. | Zbl 0926.03048

[00005] [6] R. A. Shore and T. A. Slaman, The p-T degrees of the recursive sets: lattice embeddings, extensions of embeddings and the two-quantifier theory, Theoret. Comput. Sci. 97 (1992), 263-284. | Zbl 0774.03028

[00006] [7] R. Solovay, Determinacy and type 2 recursion (abstract), J. Symbolic Logic 36 (1971), 374.

[00007] [8] G. Weitkamp, Kleene recursion over the continuum, Ph.D. Thesis, Pennsylvania State Univ., 1980.