Embedding lattices in the Kleene degrees

Hisato Muraki

Fundamenta Mathematicae (1999)

  • Volume: 162, Issue: 1, page 47-64
  • ISSN: 0016-2736

Abstract

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Under ZFC+CH, we prove that some lattices whose cardinalities do not exceed ℵ 1 can be embedded in some local structures of Kleene degrees.

How to cite

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Muraki, Hisato. "Embedding lattices in the Kleene degrees." Fundamenta Mathematicae 162.1 (1999): 47-64. <http://eudml.org/doc/212412>.

@article{Muraki1999,
abstract = {Under ZFC+CH, we prove that some lattices whose cardinalities do not exceed $ℵ_1$ can be embedded in some local structures of Kleene degrees.},
author = {Muraki, Hisato},
journal = {Fundamenta Mathematicae},
keywords = {Kleene recursive; Kleene degree; superjump},
language = {eng},
number = {1},
pages = {47-64},
title = {Embedding lattices in the Kleene degrees},
url = {http://eudml.org/doc/212412},
volume = {162},
year = {1999},
}

TY - JOUR
AU - Muraki, Hisato
TI - Embedding lattices in the Kleene degrees
JO - Fundamenta Mathematicae
PY - 1999
VL - 162
IS - 1
SP - 47
EP - 64
AB - Under ZFC+CH, we prove that some lattices whose cardinalities do not exceed $ℵ_1$ can be embedded in some local structures of Kleene degrees.
LA - eng
KW - Kleene recursive; Kleene degree; superjump
UR - http://eudml.org/doc/212412
ER -

References

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  1. [1] K. J. Devlin, Constructibility, Springer, 1984. 
  2. [2] K. Hrbáček, On the complexity of analytic sets, Z. Math. Logik Grundlag. Math. 24 (1978), 419-425. Zbl0411.03040
  3. [3] M. Lerman, Degrees of Unsolvability, Springer, 1983. 
  4. [4] H. Muraki, Local density of Kleene degrees, Math. Logic Quart. 43 (1995), 183-189. Zbl0820.03030
  5. [5] H. Muraki, Non-distributive upper semilattice of Kleene degrees, J. Symbolic Logic 64 (1999), 147-158. Zbl0926.03048
  6. [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. Zbl0774.03028
  7. [7] R. Solovay, Determinacy and type 2 recursion (abstract), J. Symbolic Logic 36 (1971), 374. 
  8. [8] G. Weitkamp, Kleene recursion over the continuum, Ph.D. Thesis, Pennsylvania State Univ., 1980. 

NotesEmbed ?

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