Steve Jackson (mathematician)

{{short description|American mathematician}}

Stephen Craig Jackson is an American set theorist at the University of North Texas.{{Cite web |title=Stephen Jackson – UNT Faculty Profile |url=https://facultyinfo.unt.edu/faculty-profile?query=Stephen+Jackson&type=name&profile=jackson&profile=jackson |access-date=2022-10-02 |website=facultyinfo.unt.edu |language=en}} Much of his most notable work has involved the descriptive set-theoretic consequences of the axiom of determinacy.{{Cite web |last=Jackson |first=Stephen Craig |title=Faculty Profile CV |url=https://facultyinfo.unt.edu/faculty-profile-cv?profile=jackson |access-date=2022-10-02 |website=facultyinfo.unt.edu |language=en}} In particular he is known for having calculated the values of all the projective ordinals (the suprema of the lengths of all prewellorderings of the real numbers 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 relations. With Dan Mauldin he solved the Steinhaus lattice problem.{{Cite journal |last=Jackson |first=Steve |last2=Mauldin |first2=R. |date=2002 |title=On a lattice problem of H. Steinhaus |url=https://www.ams.org/jams/2002-15-04/S0894-0347-02-00400-9/ |journal=Journal of the American Mathematical Society |language=en |volume=15 |issue=4 |pages=817–856 |doi=10.1090/S0894-0347-02-00400-9 |issn=0894-0347|doi-access=free }}{{Cite journal |last=Jackson |first=Steve |last2=Mauldin |first2=R. Daniel |date=2003 |title=Survey of the Steinhaus Tiling Problem |url=https://www.cambridge.org/core/journals/bulletin-of-symbolic-logic/article/abs/survey-of-the-steinhaus-tiling-problem/C2B13EA8C85AF239964FEE25D83FDDA4 |journal=Bulletin of Symbolic Logic |language=en |volume=9 |issue=3 |pages=335–361 |doi=10.2178/bsl/1058448676 |issn=1079-8986|url-access=subscription }}

Jackson earned his PhD 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 the axiom of determinacy,$$\backslash boldsymbol\{\backslash delta\}^1\_5=\backslash aleph\_\{\backslash omega^\{\backslash omega^\{\backslash omega\}\}+1\}$$ thereby solving the first Victoria Delfino problem,{{Citation |last=Caicedo |first=Andrés Eduardo |title=The fourteen Victoria Delfino problems and their status in the year 2020 |date=2020 |url=https://www.cambridge.org/core/books/large-cardinals-determinacy-and-other-topics/fourteen-victoria-delfino-problems-and-their-status-in-the-year-2020/93E409BC4A3A3EF7B93AA281C04AD45B |work=Large Cardinals, Determinacy and Other Topics: The Cabal Seminar, Volume IV |volume=4 |pages=248–280 |editor-last=Kechris |editor-first=Alexander S. |series=Lecture Notes in Logic |place=Cambridge |publisher=Cambridge University Press |isbn=978-1-107-18299-8 |last2=Löw |first2=Benedikt |editor2-last=Löwe |editor2-first=Benedikt |editor3-last=Steel |editor3-first=John R.}} one of the notorious problems of the combinatorics of the axiom of determinacy.