Download or read book Initial Segments of Degrees Below $\underline {0}^\prime $ written by Richard L. Epstein and published by American Mathematical Soc.. This book was released on 1981 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: We prove two main results: (1) [lowercase Greek]Omega + 1 is an initial segment of the degrees ([less-than or equal to]≤ a̲ for any r.e. a̲ [not equal to] 0̲ , and (2) given any 0̲ [less than] a̲ [less than] h̲ where a̲ and h̲ are r.e. and h̲ is high, there is a minimal degree m̲ [less than] h̲ such that m̲ [set-theoretic union] a̲ = h̲.