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- V. L. Selivanov
- 2001

The boolean hierarchy of partitions was introduced and studied by K. Wagner and S. Kosub, mostly over the lattice of NP -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 over some… (More)

We describe Wadge degrees of ω-languages recognizable by deterministic Turing machines. In particular, it is shown that the ordinal corresponding to these degrees is ξ where ξ = ω 1 is the first non-recursive ordinal known as the Church-Kleene ordinal. This answers a question raised in [Du0?]. 1 Formulation of Main Result Let {Σα}α<ω1 , where ω1 is the… (More)

- Victor Selivanov
- 2003

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)

- Victor L. Selivanov
- Electr. Notes Theor. Comput. Sci.
- 2008

- Victor L. Selivanov
- J. Symb. Log.
- 1995

- Victor L. Selivanov
- Theor. Comput. Sci.
- 2006

This is a survey of results in descriptive set theory for domains and similar spaces, with the emphasis on the ω-algebraic domains. We try to demonstrate that the subject is interesting in its own right and is closely related to some areas of theoretical computer science. Since the subject is still in its beginning, we discuss in detail several open… (More)

- Victor L. Selivanov
- Math. Log. Q.
- 2005

- Oleg V. Kudinov, Victor L. Selivanov
- CiE
- 2007

We prove that for any k ≥ 3 each element of the homomorphic quasiorder of finite k-labeled forests is definable, provided that the minimal non-smallest elements are allowed as parameters. As corollaries, we show that the structure is atomic and characterize the automorphism group of the structure. Similar results hold true for two other relevant structures:… (More)

We introduce and study some natural operations on the structure of finite labeled forests which is of central interest for extending the difference hierarchy to the case of partitions. It is shown that the corresponding quotient-algebra modulo the so called h-equivalence is the simplest nontrivial semilattice with discrete closures. The algebra is also… (More)

- Oleg V. Kudinov, Victor L. Selivanov, Anton V. Zhukov
- Ann. Pure Appl. Logic
- 2009