Series: Penn State Logic Seminar Date: Tuesday, April 4, 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 1 Abstract: In 1975 Chaitin and Solovay introduced $K$-triviality as a property of reals expressed in terms of prefix-free Kolmogorov complexity. In this talk we will introduce the concepts necessary for defining $K$-triviality and prove the Kraft-Chaitin theorem, an important tool for proving certain properties of $K$-trivial reals.