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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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Descriptive set theory over hyperfinite sets
The Journal of Symbolic Logic, 1989AbstractThe separation, uniformization, and other properties of the Borel and projective hierarchies over hyperfinite sets are investigated and compared to the corresponding properties in classical descriptive set theory. The techniques used in this investigation also provide some results about countably determined sets and functions, as well as an ...
H. Jerome Keisler +3 more
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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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2011
In 1905 Henri Lebesgue [1905] published a large paper Sur les fonctions representables analytiquement, which strongly influenced the next investigations in a domain of mathematics that we call today the descriptive set theory. The paper was mainly devoted to the study of the Baire Hierarchy of real functions. Moreover, a proof of one theorem was wrong (
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In 1905 Henri Lebesgue [1905] published a large paper Sur les fonctions representables analytiquement, which strongly influenced the next investigations in a domain of mathematics that we call today the descriptive set theory. The paper was mainly devoted to the study of the Baire Hierarchy of real functions. Moreover, a proof of one theorem was wrong (
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“Hyperfinite” descriptive set theory
2004Descriptive set theory studies those subsets of topological spaces (called pointsets) which can be defined, by means of a list of specified operations including, e.g., complement, countable union and intersection, projection, beginning with open sets of the space.
Vladimir Kanovei, Michael Reeken
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1997
Descriptive set theory deals with sets of reals that are described in some simple way: sets that have a simple topological structure (e.g., continuous images of closed sets) or are definable in a simple way. The main theme is that questions that are difficult to answer if asked for arbitrary sets of reals, become much easier when asked for sets that ...
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Descriptive set theory deals with sets of reals that are described in some simple way: sets that have a simple topological structure (e.g., continuous images of closed sets) or are definable in a simple way. The main theme is that questions that are difficult to answer if asked for arbitrary sets of reals, become much easier when asked for sets that ...
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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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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 and Forcing
2017Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the fourth publication in the Lecture Notes in Logic series, Miller develops the necessary ...
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