## Journal of Symbolic Logic

### Structural Properties and $\Sigma^0_2$ Enumeration Degrees

#### Abstract

We prove that each $\Sigma^0_2$ set which is hypersimple relative to $\emptyset$' is noncuppable in the structure of the $\Sigma^0_2$ enumeration degrees. This gives a connection between properties of $\Sigma^0_2$ sets under inclusion and and the $\Sigma^0_2$ enumeration degrees. We also prove that some low non-computably enumerable enumeration degree contains no set which is simple relative to $\emptyset$'.

#### Article information

Source
J. Symbolic Logic, Volume 65, Issue 1 (2000), 285-292.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183746021

Mathematical Reviews number (MathSciNet)
MR1782120

Zentralblatt MATH identifier
0945.03063

JSTOR
Nies, Andre; Sorbi, Andrea. Structural Properties and $\Sigma^0_2$ Enumeration Degrees. J. Symbolic Logic 65 (2000), no. 1, 285--292. https://projecteuclid.org/euclid.jsl/1183746021