In mathematical logic, descriptive set theory (DST) is the study of certain classes of "well-behaved" subsets of the real line and other Polish spaces...

Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any...

In descriptive set theory, a tree on a set X {\displaystyle X} is a collection of finite sequences of elements of X {\displaystyle X} such that every...

Effective descriptive set theory is the branch of descriptive set theory dealing with sets of reals having lightface definitions; that is, definitions...

In the mathematical discipline of descriptive set theory, a scale is a certain kind of object defined on a set of points in some Polish space (for example...

computability theory overlaps with proof theory and effective descriptive set theory. Basic questions addressed by computability theory include: What...

the Borel sets is called a Borel measure. Borel sets and the associated Borel hierarchy also play a fundamental role in descriptive set theory. In some...

modern topology and who contributed significantly to set theory, descriptive set theory, measure theory, and functional analysis. Hausdorff was Jewish, and...

In set theory, a tree is a partially ordered set ( T , < ) {\displaystyle (T,<)} such that for each t ∈ T {\displaystyle t\in T} , the set { s ∈ T : s...

is just as much a branch of descriptive set theory as it is of harmonic analysis. Paul J. Cohen (1958), Topics in the theory of uniqueness of trigonometrical...

Simple theorems in the algebra of sets Subset Θ (set theory) Tree (descriptive set theory) Tree (set theory) Union (set theory) Von Neumann universe Zero sharp...

inner model of V in which the axiom of determinacy holds.) Moschovakis, Yiannis N. (1980). Descriptive Set Theory. North Holland. ISBN 0-444-70199-0....

mathematician known for his work in descriptive set theory and aspects of mathematical analysis with strong connections to point-set topology. He was the eponym...

recursion theory. Descriptive set theory uses the notions of forcing from both recursion theory and set theory. Forcing has also been used in model theory, but...

ISBN 978-1-4684-9396-2. Kechris, Alexander S. (1995). Classical Descriptive Set Theory. Graduate Texts in Mathematics. Vol. 156. Springer New York, NY...

error about ten years later, and his following research has led to descriptive set theory. The fundamental mistake of Lebesgue was to think that projection...

Descriptive complexity is a branch of computational complexity theory and of finite model theory that characterizes complexity classes by the type of logic...

there a measure zero set which isn't meagre?". MathOverflow. Quintanilla, M. (2022). "The real numbers in inner models of set theory". arXiv:2206.10754...

18, 1938) is a set theorist, descriptive set theorist, and recursion (computability) theorist, at UCLA. His book Descriptive Set Theory (North-Holland)...

his contributions to ergodic theory, topological dynamics, probability theory, game theory, and descriptive set theory. Benjamin ("Benjy") Weiss was...

extension of V. Inner model theory studies the relationships of these models to determinacy, large cardinals, and descriptive set theory. Despite the name, it...

descriptive set theory, a subset of a Polish space X {\displaystyle X} is an analytic set if it is a continuous image of a Polish space. These sets were...

S. (1995), Classical Descriptive Set Theory, Berlin, New York: Springer-Verlag, ISBN 3540943749 Levy, A. (1979), Basic Set Theory, Berlin, New York: Springer-Verlag...

In descriptive set theory, the Borel determinacy theorem states that any Gale–Stewart game whose payoff set is a Borel set is determined, meaning that...

In the mathematical field of descriptive set theory, a subset of a Polish space has the perfect set property if it is either countable or has a nonempty...

topology, called the product topology. This space is commonly used in descriptive set theory, to the extent that its elements are often called "reals". It is...

In mathematical logic and descriptive set theory, the analytical hierarchy is an extension of the arithmetical hierarchy. The analytical hierarchy of formulas...

mathematical constructs of trees in graph theory, trees in set theory, and trees in descriptive set theory. A node is a structure which may contain data...

set theory such as Kripke–Platek set theory. It is an important tool in effective descriptive set theory. The central focus of hyperarithmetic theory...

in set theory, the constructible universe (or Gödel's constructible universe), denoted by L , {\displaystyle L,} is a particular class of sets that...