Alexander S. Kechris
|Institutions||California Institute of Technology|
|Doctoral advisor||Yiannis N. Moschovakis|
Alexander Sotirios Kechris (Greek : Αλέξανδρος Σωτήριος Κεχρής; born March 23, 1946) is a set theorist and logician at the California Institute of Technology.
Kechris has made contributions to the theory of Borel equivalence relations and the theory of automorphism groups of uncountable structures. His research interests cover foundations of mathematics, mathematical logic and set theory and their interactions with analysis and dynamical systems.
Kechris earned his Ph.D. in 1972 under the direction of Yiannis N. Moschovakis, with a dissertation titled Projective Ordinals and Countable Analytic Sets . During his academic career he advised 23 PhD students and sponsored 20 postdoctoral researchers.
In 2012 he became an Inaugural Fellow of the American Mathematical Society.
In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that a Cartesian product of a collection of non-empty sets is non-empty. Informally put, the axiom of choice says that given any collection of bins, each containing at least one object, it is possible to make a selection of exactly one object from each bin, even if the collection is infinite. Formally, it states that for every indexed family of nonempty sets there exists an indexed family of elements such that for every . The axiom of choice was formulated in 1904 by Ernst Zermelo in order to formalize his proof of the well-ordering theorem.
Mathematical logic, also called formal logic, is a subfield of mathematics exploring the formal applications of logic to mathematics. It bears close connections to metamathematics, the foundations of mathematics, philosophy, and theoretical computer science. The unifying themes in mathematical logic include the study of the expressive power of formal systems and the deductive power of formal proof systems.
In mathematics, model theory is the study of the relationship between formal theories, and their models, taken as interpretations that satisfy the sentences of that theory.
In mathematics, a Borel set is any set in a topological space that can be formed from open sets through the operations of countable union, countable intersection, and relative complement. Borel sets are named after Émile Borel.
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. As well as being one of the primary areas of research in set theory, it has applications to other areas of mathematics such as functional analysis, ergodic theory, the study of operator algebras and group actions, and mathematical logic.
In the mathematical discipline of general topology, a Polish space is a separable completely metrizable topological space; that is, a space homeomorphic to a complete metric space that has a countable dense subset. Polish spaces are so named because they were first extensively studied by Polish topologists and logicians—Sierpiński, Kuratowski, Tarski and others. However, Polish spaces are mostly studied today because they are the primary setting for descriptive set theory, including the study of Borel equivalence relations. Polish spaces are also a convenient setting for more advanced measure theory, in particular in probability theory.
George Whitelaw Mackey was an American mathematician known for his contributions to quantum logic, representation theory, and noncommutative geometry.
In mathematical logic, a theory is categorical if it has exactly one model. Such a theory can be viewed as defining its model, uniquely characterizing its structure.
In mathematics, a Borel equivalence relation on a Polish space X is an equivalence relation on X that is a Borel subset of X × X.
A subset of a topological space has the property of Baire, or is called an almost open set, if it differs from an open set by a meager set;
In descriptive set theory, within mathematics, Wadge degrees are levels of complexity for sets of reals. Sets are compared by continuous reductions. The Wadge hierarchy is the structure of Wadge degrees. These concepts are named after William W. Wadge.
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 one of the two players will have a winning strategy for the game.
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. Scales were originally isolated as a concept in the theory of uniformization, but have found wide applicability in descriptive set theory, with applications such as establishing bounds on the possible lengths of wellorderings of a given complexity, and showing that there are largest countable sets of certain complexities.
Stevo Todorčević, is a Yugoslavian mathematician specializing in mathematical logic and set theory. He holds a Canada Research Chair in mathematics at the University of Toronto, and a director of research position at the Centre national de la recherche scientifique in Paris.
Benjamin Weiss is an American-Israeli mathematician known for his contributions to ergodic theory, topological dynamics, probability theory, game theory, and descriptive set theory.
Roy Lee Adler was an American mathematician.
In mathematics, structural Ramsey theory is a categorical generalisation of Ramsey theory, rooted in the idea that many important results of Ramsey theory have "similar" logical structure. The key observation is noting that these Ramsey-type theorems can be expressed as the assertion that a certain category has the Ramsey property.