Biography:Steve Jackson (mathematician)
Steve Jackson (full name: Stephen Craig Jackson) is an American set theorist at the University of North Texas.[1] Much of his most notable work has involved the descriptive set-theoretic consequences of the axiom of determinacy.[2] 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.[3][4]
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,[math]\displaystyle{ \mathbf{\delta^1_5}=\aleph_{\omega^{\omega^{\omega}}+1} }[/math] thereby solving the first Victoria Delfino problem,[5] one of the notorious problems of the combinatorics of the axiom of determinacy.
References
- ↑ "Stephen Jackson – UNT Faculty Profile" (in en). https://facultyinfo.unt.edu/faculty-profile?query=Stephen+Jackson&type=name&profile=jackson&profile=jackson.
- ↑ Jackson, Stephen Craig. "Faculty Profile CV" (in en). https://facultyinfo.unt.edu/faculty-profile-cv?profile=jackson.
- ↑ Jackson, Steve; Mauldin, R. (2002). "On a lattice problem of H. Steinhaus" (in en). Journal of the American Mathematical Society 15 (4): 817–856. doi:10.1090/S0894-0347-02-00400-9. ISSN 0894-0347. https://www.ams.org/jams/2002-15-04/S0894-0347-02-00400-9/.
- ↑ Jackson, Steve; Mauldin, R. Daniel (2003). "Survey of the Steinhaus Tiling Problem" (in en). Bulletin of Symbolic Logic 9 (3): 335–361. doi:10.2178/bsl/1058448676. ISSN 1079-8986. https://www.cambridge.org/core/journals/bulletin-of-symbolic-logic/article/abs/survey-of-the-steinhaus-tiling-problem/C2B13EA8C85AF239964FEE25D83FDDA4.
- ↑ Caicedo, Andrés Eduardo; Löw, Benedikt (2020), Kechris, Alexander S.; Löwe, Benedikt; Steel, John R., eds., "The fourteen Victoria Delfino problems and their status in the year 2020", Large Cardinals, Determinacy and Other Topics: The Cabal Seminar, Volume IV, Lecture Notes in Logic (Cambridge: Cambridge University Press) 4: pp. 248–280, ISBN 978-1-107-18299-8, https://www.cambridge.org/core/books/large-cardinals-determinacy-and-other-topics/fourteen-victoria-delfino-problems-and-their-status-in-the-year-2020/93E409BC4A3A3EF7B93AA281C04AD45B
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