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The minimal complementation property above 0′

✍ Scribed by Andrew E. M. Lewis

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
383 KB
Volume
51
Category
Article
ISSN
0044-3050

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✦ Synopsis

Abstract

Let us say that any (Turing) degree d > 0 satisfies the minimal complementation property (MCP) if for every degree 0 < a < d there exists a minimal degree b < d such that a ∨ b = d (and therefore a ∧ b = 0). We show that every degree d ≥ 0′ satisfies MCP. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

📜 SIMILAR VOLUMES

Properly Σ2 minimal degrees and 0″ compl
Properly Σ2 minimal degrees and 0″ complementation
✍ S. Barry Cooper; Andrew E. M. Lewis; Yue Yang 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 96 KB

We show that there exists a properly Σ2 minimal (Turing) degree b, and moreover that b can be chosen to join with 0 to 0 -so that b is a 0 complement for every degree a such that 0 ≤ a < 0 .