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.

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