Steve Jackson (mathematician)
Encyclopedia
Steve Jackson is a set theorist
at University of North Texas
. Much of his most notable work has involved the descriptive set-theoretic
consequences of the axiom of determinacy
. In particular he is known for having calculated the values of all the projective ordinals (the suprema of the lengths of all prewellordering
s of the reals at a particular level in the projective hierarchy) under the assumption that the axiom of determinacy holds.
In recent years he has also made contributions to the theory of Borel equivalence relation
s. With Dan Mauldin he solved the Steinhaus lattice problem.
Jackson earned his Ph.D.
in 1983 at UCLA under the direction of Donald A. Martin
, with a dissertation on A Calculation of δ15. In it, he proved that, under AD,
thereby solving the first Victoria Delfino problem, one of the notorious problems of the combinatorics of the axiom of determinacy
.
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
at University of North Texas
University of North Texas
The University of North Texas is a public institution of higher education and research in Denton. Founded in 1890, UNT is part of the University of North Texas System. As of the fall of 2010, the University of North Texas, Denton campus, had a certified enrollment of 36,067...
. Much of his most notable work has involved the descriptive set-theoretic
Descriptive set theory
In mathematical logic, descriptive set theory is the study of certain classes of "well-behaved" subsets of the real line and other Polish spaces...
consequences of the axiom of determinacy
Axiom of determinacy
The axiom of determinacy is a possible axiom for set theory introduced by Jan Mycielski and Hugo Steinhaus in 1962. It refers to certain two-person games of length ω with perfect information...
. In particular he is known for having calculated the values of all the projective ordinals (the suprema of the lengths of all prewellordering
Prewellordering
In set theory, a prewellordering is a binary relation that is transitive, wellfounded, and total. In other words, if \leq is a prewellordering on a set X, and if we define \sim byx\sim y\iff x\leq y \land y\leq x...
s of the reals at a particular level in the projective hierarchy) under the assumption that the axiom of determinacy holds.
In recent years he has also made contributions to the theory of Borel equivalence relation
Borel equivalence relation
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....
s. With Dan Mauldin he solved the Steinhaus lattice problem.
Jackson earned his Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
in 1983 at UCLA under the direction of Donald A. Martin
Donald A. Martin
Donald A. Martin is a set theorist and philosopher of mathematics at UCLA, where he is a member of the faculty of mathematics and philosophy....
, with a dissertation on A Calculation of δ15. In it, he proved that, under AD,
thereby solving the first Victoria Delfino problem, one of the notorious problems of the combinatorics of the axiom of determinacy
Axiom of determinacy
The axiom of determinacy is a possible axiom for set theory introduced by Jan Mycielski and Hugo Steinhaus in 1962. It refers to certain two-person games of length ω with perfect information...
.
External links
- List of papers published by Steve Jackson
- Steve Jackson at the Mathematics Genealogy ProjectMathematics Genealogy ProjectThe Mathematics Genealogy Project is a web-based database for the academic genealogy of mathematicians. As of September, 2010, it contained information on approximately 145,000 mathematical scientists who contribute to "research-level mathematics"...