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Generalized descriptive set theory and classification theory [PDF]
Memoirs of the American Mathematical Society, 2013 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-David +2 more
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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 ...
Kechris, Alexander S.
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Omitting types: application to descriptive set theory [PDF]
Proceedings of the American Mathematical Society, 1975 The omitting types theorem of infinitary logic is used to prove that every small Π 1
Richard Mansfield
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Topology and descriptive set theory [PDF]
Topology and its Applications, 1994 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kechris, Alexander S.
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THE USE OF COMPLEXITY HIERARCHIES IN DESCRIPTIVE SET THEORY AND AUTOMATA THEORY [PDF]
TASK Quarterly, 2005 The concept of a reduction between subsets of a given space is described, giving rise to various complexity hierarchies, studied both in descriptive set theory and in automata theory.
ALESSANDRO ANDRETTA, RICCARDO CAMERLO
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Explanation in Descriptive Set Theory [PDF]
Abstract In this paper we investigate explanatory proofs in mathematics. We do this via an extended case study from descriptive set theory. The aim is to shed light on what makes explanatory proofs explanatory. Building on earlier work, we argue that there may be more than one notion of explanation in operation in mathematics: there does
Carolin Antos, Mark Colyvan
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Descriptive Set Theory and Computable Topology (Dagstuhl Seminar 21461) [PDF]
, 2022 Computability and continuity are closely linked - in fact, continuity can be seen as computability relative to an arbitrary oracle. As such, concepts from topology and descriptive set theory feature heavily in the foundations of computable analysis ...
Hoyrup, Mathieu +3 more
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Rate Distortion Theory for Descriptive Statistics [PDF]
, 2022 Rate distortion theory was developed for optimizing lossy compression of data, but it also has a lot of applications in statistics. In this paper we will see how rate distortion theory can be used to analyze a complicated data set involving orientations ...
Harremoës, Peter, Peter Harremoës
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Views from a peak:Generalisations and descriptive set theory [PDF]
, 2023 This dissertation has two major threads, one is mathematical, namely descriptive set theory, the other is philosophical, namely generalisation in mathematics.
Wontner, N.J.H.
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Venn diagrams and probability in clinical research
Сеченовский вестник, 2020 Statistics is the science dealing with the collecting, summarizing and interpreting of associations in research data, and has a leading role in medical research.
N. М. Bulanov +6 more
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