Victor L. Selivanov

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The boolean hierarchy of partitions was introduced and studied by K. W agner and S. Kosub, mostly over the lattice of N P-sets. We consider this hierarchy for the case of lattices having the reduction property and show that in this case the hierarchy behaves much easier and admits a deeper investigation. We completely characterize the hierarchy o v er some(More)
By applying descriptive set theory to the Wagner's fine structure of regular ω-languages we get quite different proofs of his results and obtain new results. We give an automata-free description of the fine structure. We present also a simple property of a deterministic Muller automaton equivalent to the condition that the corresponding regular ω-language(More)
The structure of the Wadge degrees on zero-dimensional spaces is very simple (almost well-ordered), but for many other natural non-zero-dimensional spaces (including the space of reals) this structure is much more complicated. We consider weaker notions of reducibility, including the so-called ∆ 0 α-reductions, and try to find for various natural(More)
We prove that the homomorphic quasiorder of finite k-labeled forests has a hereditary undecidable first-order theory for k ≥ 3, in contrast to the known decidability result for k = 2. We establish also hereditary undecidability (again for every k ≥ 3) of first-order theories of two other relevant structures: the homomorphic quasiorder of finite k-labeled(More)