Steve Jackson (full name: Stephen Craig Jackson) is an American set theorist at the

University of North Texas The University of North Texas (UNT) is a public research university in Denton, Texas. It was founded as a nonsectarian, coeducational, private teachers college in 1890 and was formally adopted by the state 11 years later."Denton Normal School," ...

. Much of his most notable work has involved the descriptive set-theoretic consequences of the

axiom of determinacy In mathematics, the axiom of determinacy (abbreviated as AD) is a possible axiom for set theory introduced by Jan Mycielski and Hugo Steinhaus in 1962. It refers to certain two-person topological games of length ω. AD states that every game of ...

. In particular he is known for having calculated the values of all the projective ordinals (the suprema of the lengths of all

prewellordering In set theory, a prewellordering on a set X is a preorder \leq on X (a transitive and strongly connected relation on X) that is wellfounded in the sense that the relation x \leq y \land y \nleq x is wellfounded. If \leq is a prewellordering on ...

s of the

real number In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every real ...

s at a particular level in the

projective hierarchy In the mathematical field of descriptive set theory, a subset A of a Polish space X is projective if it is \boldsymbol^1_n for some positive integer n. Here A is * \boldsymbol^1_1 if A is analytic * \boldsymbol^1_n if the complement of A, X\set ...

) under the assumption that the axiom of determinacy holds. In recent years he has also made contributions to the theory of

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'' (in the product topology). Formal definition Given Borel equivalence relations ''E'' and '' ...

s. With Dan Mauldin he solved the Steinhaus lattice problem. Jackson earned his PhD in 1983 at

UCLA The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California. UCLA's academic roots were established in 1881 as a teachers college then known as the southern branch of the California St ...

under the direction of

Donald A. Martin Donald Anthony Martin (born December 24, 1940), also known as Tony Martin, is an American set theorist and philosopher of mathematics at UCLA, where he is an emeritus professor of mathematics and philosophy. Education and career Martin rece ...

, with a dissertation on ''A Calculation of'' δ¹₅. In it, he proved that, under the axiom of determinacy,

\mathbf=\aleph_

thereby solving the first Victoria Delfino problem, one of the notorious problems of the combinatorics of the

References

External links

List of papers published by Steve Jackson
* University of California, Los Angeles alumni University of North Texas faculty 20th-century American mathematicians 21st-century American mathematicians Living people Year of birth missing (living people) Set theorists {{US-mathematician-stub