A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2008; you can also visit the original URL.
The file type is application/pdf
.
DIRECT AND LOCAL DEFINITIONS OF THE TURING JUMP
2007
Journal of Mathematical Logic
We show that there are 5 formulas in the language of the Turing degrees, D, with ,_ and^, that de...ne the relations x 00 y 00 , x 00 = y 00 and so x 2 L 2 (y) = fx yjx 00 = y 00 g in any jump ideal containing 0 (!) . There are also 6 & 6 and 8 formulas that de...ne the relations w = x 00 and w = x 0 , respectively, in any such ideal I. In the language with just the quanti...er complexity of each of these de...nitions increases by one. For a lower bound on de...nability, we show that no 2 or 2
doi:10.1142/s0219061307000676
fatcat:ymhxmsnwjrbidpz3q3krj3emvi