Saturday, April 2, 201610:45 amNERDS: New England Recursion & Definability SeminarLocklin Hall, Room 232, Springfield College

# A one-generic that does not compute a modulus for one-genericity

## Marcia Groszek

### Dartmouth College

A function *g ∈ 2 ^{ω}* is 1-generic if, for every recursively enumerable

*W⊂ 2*, there is some

^{< ω}*σ⊂ g*such that either

*σ∈W*or σ has no extensions in

*W*. That is, any possible Σ

^{0}

_{1}property of

*g*is either forced to be true or forced to be false by some finite initial segment of

*g*. A function

*f∈ω*is a modulus for 1-genericity if, whenever

^{ω}*h*pointwise dominates

*f*, then

*h*computes some 1-generic. If

*g*is 1-generic and either Δ

^{0}

_{2}-definable or 2-generic, then

*g*computes a modulus for 1-genericity. We give a priority argument to produce a 1-generic

*g*that does not compute a modulus for 1-genericity.

(Joint work with Theodore A. Slaman.)

Marcia Groszek is a professor on the faculty of Dartmouth College.