On the Wadge reducibility of k-partitions

Victor L. Selivanov
2010 The Journal of Logic and Algebraic Programming  
Dedicated to Dieter Spreen on the occasion of his 60th birthday Keywords: Baire space Baire domain Wadge reducibility k-partition Discrete weak semilattice Forest Homomorphic preorder We establish some results on the Wadge degrees and on the Boolean hierarchy of k-partitions of some spaces, where k is a natural number. The main attention is paid to the Baire space, Baire domain and their close relatives. For the case of 0 2 -measurable k-partitions the structures of Wadge degrees are
more » ... ed completely. For many degree structures, undecidability of the first-order theories is shown, for any k ≥ 3.
doi:10.1016/j.jlap.2009.02.008 fatcat:gkqlz6arwrcabjqavzeg2d4p5m