General Topology-I

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Classical Descriptive Set Theory

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Aspects of topology: On dimension theory

Preface 1. Fourier series and Fourier transforms 2. Distributions 3. Elliptic equations (fundamental theory) 4. Initial value problems (Cauchy problems) 5. Evolution equations 6. Hyperbolic equations 7. Semi-linear hyperbolic equations 8. Green's functions and spectra Supplementary remarks Guide to the literature Bibliography Symbols Index.

The theory of partial differential equations

The Department of Languages provides a vital component in the undergraduate liberal arts education offered at the University of WisconsinEau Claire. The department promotes multilingualism as the key to intercultural understanding. It does so through courses in foreign language, culture, and literature, including English language for native speakers of other languages; major and minor programs in a number of world languages; study abroad opportunities and internships in many countries; and student/faculty collaborative research. Graduates from the Department of Languages serve at home and abroad as ambassadors for a diverse, peacefully interacting global society.

Ω-languages

We consider fine hierarchies in recursion theory, descriptive set theory, logic and complexity theory. The main results state that the sets of values of different Boolean terms coincide with the levels of suitable fine hierarchies. This gives new short descriptions of these hierarchies and shows that collections of sets of values of Boolean terms are almost well ordered by inclusion. For the sake of completeness we mention also some earlier results demonstrating the usefulness of fine hierarchies.

https://www.jstor.org/stable/pdfplus/2275522.pdf

Fine hierarchies and Boolean terms

Towards a descriptive set theory for domain-like structures

https://link.springer.com/content/pdf/10.1007/3-540-59293-8_201.pdf

Fine hierarchy of regular Ω-languages

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 ω where
 ξ = ω 1 CK is the first non-recursive ordinal known as the
 Church–Kleene ordinal. This answers a question raised in [2].

Wadge Degrees of ω-Languages of Deterministic Turing Machines

Attempts to extend the classical Hausdorff difference hierarchy to the case of partitions of a space to k > 2 subsets lead to non-equivalent notions. In a hope to identify the right extension we consider the extensions appeared in the literature so far: the limit-, level-, Boolean and Wadge hierarchies of k -partitions. The advantages and disadvantages of the four hierarchies are discussed. The main technical contribution of this paper is a complete characterization of the Wadge degrees of [ ? ] o 2-measurable k -partitions of the Baire space.

Victor L. Selivanov

Papers

Fine hierarchies and Boolean terms

Towards a descriptive set theory for domain-like structures

Fine hierarchy of regular Ω-languages

Wadge Degrees of ω-Languages of Deterministic Turing Machines

Hierarchies of Δ02-measurable k -partitions