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Descriptive Set Theory and the Structure of Sets of Uniqueness
1987The study of sets of uniqueness for trigonometric series has a long history, originating in the work of Riemann, Heine, and Cantor in the mid-nineteenth century. Since then it has been a fertile ground for numerous investigations involving real analysis, classical and abstract harmonic analysis, measure theory, functional analysis and number theory. In
Kechris, Alexander S., Louveau, Alain
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Learning Theory and Descriptive Set Theory
Journal of Logic and Computation, 1993Kevin T. Kelly. Learning Theory and Descriptive Set Theory.
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1970
The notion of a ‘set’, or collection of objects, is basic, both in our daily lives and in mathematics. As we grow up, we become aware of collections of toys, groups of people, families of relatives, heaps of sand, classes of schoolchildren, mobs of rioters, and whole lists of collective nouns.
H. B. Griffiths, P. J. Hilton
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The notion of a ‘set’, or collection of objects, is basic, both in our daily lives and in mathematics. As we grow up, we become aware of collections of toys, groups of people, families of relatives, heaps of sand, classes of schoolchildren, mobs of rioters, and whole lists of collective nouns.
H. B. Griffiths, P. J. Hilton
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Analytic sets in Descriptive Set Theory and NP sets in Complexity Theory
Fundamenta Informaticae, 2002Motivated by the analogy ``(NP/Poly)∼analytic'', we propose a co-analytic set W whose finite equivalent W_finite is coNP-complete. The complement of W is in fact a variant of ``infinite clique''. A combinatorial proof of the non-analyticity of W is produced and studied in order to be (eventually) ``finitized'' into a probabilistic proof of ``W_finite ∉
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Descriptive Set Theory: Projective Sets
1977Publisher Summary This chapter describes classical and effective descriptive set theory, with emphasis mainly on projective sets. The chapter provides an account of the revival in this subject that has taken place in the past 10 years, a revival based on strong set theoretic hypotheses—notably, projective determinacy.
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