Non-Distributive Upper Semilattice of Kleene Degrees
Muraki, Hisato
J. Symbolic Logic, Tome 64 (1999) no. 1, p. 147-158 / Harvested from Project Euclid
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$\mathscr{K}$ denotes the upper semilattice of all Kleene degrees. Under ZF + AD + DC, $\mathscr{K}$ is well-ordered and deg(X$^{SJ}$) is the next Kleene degree above deg(X) for $X \subseteq\omega\omega$ (see [4] and [5. Chapter V]). While, without AD, properties of $\mathscr{K}$ are not always clear. In this note, we prove the non-distributivity of $\mathscr{K}$ under ZFC ($\S$1), and that of Kleene degrees between deg(X) and deg(X$^{SJ}$) for some X under ZFC + CH ($\S$2,3).
Publié le : 1999-03-14
Classification:  
@article{1183745697,
     author = {Muraki, Hisato},
     title = {Non-Distributive Upper Semilattice of Kleene Degrees},
     journal = {J. Symbolic Logic},
     volume = {64},
     number = {1},
     year = {1999},
     pages = { 147-158},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183745697}
}

Muraki, Hisato. Non-Distributive Upper Semilattice of Kleene Degrees. J. Symbolic Logic, Tome 64 (1999) no. 1, pp.  147-158. http://gdmltest.u-ga.fr/item/1183745697/