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- V. L. Selivanov
- 2001

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)

- 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)

We describe Wadge degrees of ω-languages recognizable by determin-istic Turing machines. In particular, it is shown that the ordinal corresponding to these degrees is ξ ω where ξ = ω CK 1 is the first non-recursive ordinal known as the Church-Kleene ordinal. This answers a question raised in [Du0?]. 0 α } α<ω1 , where ω 1 is the first uncountable ordinal,… (More)

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)

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)

We propose a new, logical, approach to the decidability problem for the Straubing and Brzozowski hierarchies based on the preservation theorems from model theory, on a theorem of Higman, and on the Rabin tree theorem. In this way, we get purely logical, short proofs for some known facts on decidability, which might be of methodological interest. Our… (More)

Introduction Investigation of the infinite behavior of computing devices is of great interest for computer science because many hardware and software concurrent systems (like processors or operating systems) may not terminate. The study of infinite computations is important for several branches of theoretical computer science, including verification and… (More)