Embedding lattices in the Kleene degrees

Hisato Muraki

Fundamenta Mathematicae (1999)

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

Abstract

top
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

top

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

top
  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 ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.