# Automorphisms of the truth-table degrees are fixed on some cone - Mathematics > Logic

Automorphisms of the truth-table degrees are fixed on some cone - Mathematics > Logic - Download this document for free, or read online. Document in PDF available to download.

Abstract: Let Dtt denote the set of truth-table degrees. A bijection p from Dtt to Dttis an automorphism if for all truth-table degrees x and y we have x <=tt y ifand only if px <=tt py. We say an automorphism p is fixed on some cone ifthere is a degree b such that for all x >=tt b we have px = x. We first provethat for every 2-generic real X we have X- is not tt below X + 0-. We nextprove that for every real X >=tt 0- there is a real Y such that Y + 0- =tt Y-=tt X. Finally, we use this to demonstrate that every automorphism of thetruth-table degrees is fixed on some cone.

Author: ** Bernard A. Anderson**

Source: https://arxiv.org/