Recursively Enumerable Sets and Degrees
نویسندگان
چکیده
TABLE OF CONTENTS Introduction Chapter I. The relation of the structure of an r.e. set to its degree. 1. Post's program and simple sets. 2. Dominating functions and quotient lattices. 3. Maximal sets and high degrees. 4. Low degrees, atomless sets, and invariant degree classes. 5. Incompleteness and completeness for noninvariant properties. Chapter II. The structure, automorphisms, and elementary theory of the r.e. sets. 6. Basic facts and splitting theorems. 7. Hh-simple sets. 8. Major subsets and r-maximal sets. 9. Automorphisms of &. 10. The elementary theory of S. Chapter III. The structure of the r.e. degrees. 11. Basic facts. 12. The finite injury priority method. 13. The infinite injury priority method. 14. The minimal pair method and lattice embeddings in R. 15. Cupping and splitting r.e. degrees. 16. Automorphisms and decidability of R.
منابع مشابه
CDMTCS Research Report Series Difference Splittings of Recursively Enumerable Sets
We study here the degree-theoretic structure of set-theoretical splittings of recursively enumerable (r.e.) sets into differences of r.e. sets. As a corollary we deduce that the ordering of wtt–degrees of unsolvability of differences of r.e. sets is not a distributive semilattice and is not elementarily equivalent to the ordering of r.e. wtt–degrees of unsolvability.
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