The Turing Closure of an Archimedean Field

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

• Type: Conference
• Year: 1998
• Where: MCU
• Authors: Paolo Boldi, Sebastiano Vigna
• Keywords: -uniformly Decidable Sets, Archimedean Fields, MCU 1998, MCU 2007, Turing Machines