Differences of Computably Enumerable Sets

نویسندگان

Steffen Lempp

André Nies

چکیده

We consider the lower semilattice D of diierences of c.e. sets under inclusion. It is shown that D is not distributive as a semilattice, and that the c.e. sets form a deenable subclass.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Definable encodings in the computably enumerable sets

The purpose of this communication is to announce some recent results on the computably enumerable sets. There are two disjoint sets of results; the first involves invariant classes and the second involves automorphisms of the computably enumerable sets. What these results have in common is that the guts of the proofs of these theorems uses a new form of definable coding for the computably enume...

متن کامل

Universal computably enumerable sets and initial segment prefix-free complexity

We show that there are Turing complete computably enumerable sets of arbitrarily low non-trivial initial segment prefix-free complexity. In particular, given any computably enumerable set A with non-trivial prefixfree initial segment complexity, there exists a Turing complete computably enumerable set B with complexity strictly less than the complexity of A. On the other hand it is known that s...

متن کامل

The global structure of computably enumerable sets

We will work in the structure of the computably enumerable sets. The language is just inclusion, ⊆. This structure is called E. Our quest is to partially survey our current understanding of the global structure of E and the relationship between E and the computably enumerable degrees and to pose questions whose answers should provide further insight.

متن کامل

On the filter of computably enumerable supersets of an r-maximal set

We study the lter L (A) of computably enumerable supersets (modulo nite sets) of an r-maximal set A and show that, for some such set A, the property of being co nite in L (A) is still 0 3 -complete. This implies that for this A, there is no uniformly computably enumerable \tower" of sets exhausting exactly the coin nite sets in L (A).

متن کامل

Kolmogorov complexity and computably enumerable sets

We study the computably enumerable sets in terms of the: (a) Kolmogorov complexity of their initial segments; (b) Kolmogorov complexity of finite programs when they are used as oracles. We present an extended discussion of the existing research on this topic, along with recent developments and open problems. Besides this survey, our main original result is the following characterization of the ...

متن کامل