Cuppability of Simple and Hypersimple Sets
نویسندگان
چکیده
An incomplete degree is cuppable if it can be joined by an incomplete degree to a complete degree. For sets fulfilling some type of simplicity property one can now ask whether these sets are cuppable with respect to a certain type of reducibilities. Several such results are known. In this paper we settle all the remaining cases for the standard notions of simplicity and all the main strong reducibilities. There are two sides to every question. —Protagoras, quoted in Diogenes Laertius, Lives of Eminent Philosophers.
منابع مشابه
Hypersimplicity and semicomputability in the weak truth table degrees
We study the classes of hypersimple and semicomputable sets as well as their intersection in the weak truth table degrees. We construct degrees that are not bounded by hypersimple degrees outside any non-trivial upper cone of Turing degrees and show that the hypersimple-free c.e. wtt degrees are downwards dense in the c.e. wtt degrees. Moreover, we consider the sets that are both hypersimple an...
متن کاملCdmtcs Research Report Series on Hypersimple Sets and Chaitin Complexity on Hypersimple Sets and Chaitin Complexity
In this paper we study some computability theoretic properties of two notions of randomness for nite strings: randomness based on the blank-endmarker complexity measure and Chaitin randomness based on the self-delimiting complexity measure. For example, we nd the position of RAND and RAND at the same level in the scale of immunity notions by proving that both of them are not hyperimmune sets. A...
متن کاملThe Hypersimple-Free C.E. WTT Degrees Are Dense in the C.E. WTT Degrees
We show that in the c.e. weak truth table degrees if b < c then there is an a which contains no hypersimple set and b < a < c. We also show that for every w < c in the c.e. wtt degrees such that w is hypersimple, there is a hypersimple a such that w < a < c. On the other hand we know that there are intervals which contain no hypersimple set.
متن کاملEffectively Simple Sets
We use the word "number" to mean positive integer, and "set" to mean set of positive integers. A set a is called simple (after Post [l ]) iff a is r.e. (recursively enumerable), infinite, and its complement à, though infinite, contains no infinite recursively enumerable subset. We shall call a set a effectively simple if a and its complement are infinite, a is r.e., and there exists a recursive...
متن کاملTwo Notes on Recursively Enumerable Sets
Introduction. These notes are based on E. L. Post's paper Recursively enumerable sets of positive integers and their decision problems1 to which we shall refer as RES. The reader is assumed to be familiar with §§1-5 and 9 of this paper. In the first note we shall discuss some algebraic properties of simple and hypersimple sets. In the second note we shall prove the existence of a recursively en...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Notre Dame Journal of Formal Logic
دوره 48 شماره
صفحات -
تاریخ انتشار 2007