Logic Colloquium 2008

Tamás MátraiOn a new construction of \sigma-ideals of compact setsAlfréd Rényi Institute of Mathematics, Reáltanoda street 13-15, 1053 Budapest, Hungary matrait@renyi.hu

We present a new construction of \bf{\Pi}^{{0}}_{{2}} \sigma-ideals of compact sets. To shed light on the role of this construction, we take a tour of the recent developments of the theory of \sigma-ideals of compact sets. We are mainly concerned with open and recently solved problems related to regularity properties and Tuckey reducibility.