Series: Penn State Logic Seminar Date: Tuesday, April 18, 2006 Time: 2:30 - 3:45 PM Place: 106 McAllister Building Speaker: Esteban Gomez-Riviere, Penn State, Mathematics Title: Introduction to $K$-Trivial Reals, part 3 Abstract: In previous talks we introduced $K$-trivial reals and saw that they are $\Delta^0_2$. In this talk we shall construct a non-recursive, recursively enumerable, $K$-trivial real. We shall then introduce other related lowness properties and examine some of the relations among them. These properties of being strongly-$K$-trivial, low-for-random, and basic-for-random have been recently shown to be equivalent. This result is due primarily to Andre Nies.