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New Directions in Descriptive Set Theory [PDF]
Bulletin of Symbolic Logic, 1999 §1. I will start with a quick definition of descriptive set theory: It is the study of the structure of definable sets and functions in separable completely metrizable spaces. Such spaces are usually calledPolish spaces. Typical examples are ℝn, ℂn, (separable) Hilbert space and more generally all separable Banach spaces, theCantor space2ℕ, theBaire ...
Alexander S. Kechris
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Hierarchies of Effective Descriptive Set Theory [PDF]
Transactions of the American Mathematical Society, 1969 1. Introduction and summary. The theory of hierarchies deals with the classification of objects according to some measure of their complexity. Such classifications have been fruitful in several areas of mathematics: analysis (descriptive set theory), recursion theory, and the theory of models.
Peter G. Hinman
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Generalized Descriptive Set Theory and Classification Theory [PDF]
Memoirs of the American Mathematical Society, 2010 Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper we study the generalization where countable is replaced by uncountable. We explore properties of generalized Baire and Cantor spaces, equivalence relations and their Borel reducibility.
Friedman, Sy D. +2 more
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The descriptive set-theoretic complexity of the set of points of continuity of a multi-valued function (Extended Abstract) [PDF]
Electronic Proceedings in Theoretical Computer Science, 2010 In this article we treat a notion of continuity for a multi-valued function F and we compute the descriptive set-theoretic complexity of the set of all x for which F is continuous at x.
Vassilios Gregoriades
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MathematicsThe following two consequences of the axiom of constructibility V=L will be established for every n≥3: 1. Every linear Σn1 set is the projection of a uniform planar Πn−11 set. 2.
Vladimir Kanovei, Vassily Lyubetsky
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Topology and descriptive set theory
Topology and its Applications, 1994 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alexander S. Kechris
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The descriptive set-theoretic complexity of the set of points of continuity of a multi-valued function [PDF]
Logical Methods in Computer Science, 2011 In this article we treat a notion of continuity for a multi-valued function $F$ and we compute the descriptive set-theoretic complexity of the set of all $x$ for which $F$ is continuous at $x$.
Vassilios Gregoriades
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Descriptive set Theory of Families of Small Sets [PDF]
Bulletin of Symbolic Logic, 2007 AbstractThis is a survey paper on the descriptive set theory of hereditary families of closed sets in Polish spaces. Most of the paper is devoted to ideals and σ-ideals of closed or compact sets.
Matheron, Étienne, Zelený, Miroslav
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On the Uniform Projection Problem in Descriptive Set Theory
AxiomsFor every n≥1, generic models of ZFC will be presented for either of the following two sentences: 1. There exists a linear Σn+21 set not equal to the projection of any uniform planar Πn+21 set. 2.
Vladimir Kanovei, Vassily Lyubetsky
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Mixing and descriptive set theory [PDF]
Illinois Journal of Mathematics, 2006 A complete analytic set is defined through the concepts of invariant measure ...
Robert Kaufman
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