The turing closure of an archimedean field

✍ Scribed by Paolo Boldi; Sebastiano Vigna

• Book ID: 104326767
• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 124 KB
• Volume: 231
• Category: Article
• ISSN: 0304-3975
• DOI: 10.1016/s0304-3975(99)00096-1

✦ Synopsis

A BSS machine is -uniform if it does not use exact tests; such machines are equivalent (modulo parameters) to Type 2 Turing machines. We deÿne a notion of closure related to Turing machines for archimedean ÿelds, and show that such ÿelds admit nontrivial -uniformly decidable sets i they are not Turing closed. Then, the partially ordered set of Turing closed ÿelds is proved isomorphic to the ideal completion of unsolvability degrees.