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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 δでるた¹₅. In it, he proved that, under the axiom of determinacy,

\mathbf {\delta _{5}^{1}} =\aleph _{\omega ^{\omega ^{\omega }}+1}

thereby solving the first Victoria Delfino problem,^[5] one of the notorious problems of the combinatorics of the axiom of determinacy.

References[edit]

^ "Stephen Jackson – UNT Faculty Profile". facultyinfo.unt.edu. Retrieved 2022-10-02.
^ Jackson, Stephen Craig. "Faculty Profile CV". facultyinfo.unt.edu. Retrieved 2022-10-02.
^ Jackson, Steve; Mauldin, R. (2002). "On a lattice problem of H. Steinhaus". Journal of the American Mathematical Society. 15 (4): 817–856. doi:10.1090/S0894-0347-02-00400-9. ISSN 0894-0347.
^ Jackson, Steve; Mauldin, R. Daniel (2003). "Survey of the Steinhaus Tiling Problem". Bulletin of Symbolic Logic. 9 (3): 335–361. doi:10.2178/bsl/1058448676. ISSN 1079-8986.
^ 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, vol. 4, Cambridge: Cambridge University Press, pp. 248–280, ISBN 978-1-107-18299-8

External links[edit]

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[1] "Stephen Jackson – UNT Faculty Profile". facultyinfo.unt.edu. Retrieved 2022-10-02.

[2] Jackson, Stephen Craig. "Faculty Profile CV". facultyinfo.unt.edu. Retrieved 2022-10-02.

[3] Jackson, Steve; Mauldin, R. (2002). "On a lattice problem of H. Steinhaus". Journal of the American Mathematical Society. 15 (4): 817–856. doi:10.1090/S0894-0347-02-00400-9. ISSN 0894-0347.

[4] Jackson, Steve; Mauldin, R. Daniel (2003). "Survey of the Steinhaus Tiling Problem". Bulletin of Symbolic Logic. 9 (3): 335–361. doi:10.2178/bsl/1058448676. ISSN 1079-8986.

[5] 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, vol. 4, Cambridge: Cambridge University Press, pp. 248–280, ISBN 978-1-107-18299-8

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+{{short description|American mathematician}}
-'''Steve Jackson''' (full name: '''Stephen Craig Jackson''') is a [[set theory|set theorist]] at [[University of North Texas]]. Much of his most notable work has involved the [[descriptive set theory|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.
+'''Steve Jackson''' (full name: '''Stephen Craig Jackson''') is an American [[set theory|set theorist]] at the [[University of North Texas]].<ref>{{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}}</ref> Much of his most notable work has involved the [[descriptive set theory|descriptive set-theoretic]] consequences of the [[axiom of determinacy]].<ref>{{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}}</ref> 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 [[real number]]s 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]].<ref>{{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 }}</ref><ref>{{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 }}</ref>
-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 PhD in 1983 at [[UCLA]] under the direction of [[Donald A. Martin]], with a [[dissertation]] on ''A Calculation of'' '''δでるた'''<sup>1</sup><sub>5</sub>. In it, he proved that, under the axiom of determinacy,<math display="block">\mathbf{\delta^1_5}=\aleph_{\omega^{\omega^{\omega}}+1}</math> thereby solving the first Victoria Delfino problem,<ref>{{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.}}</ref> one of the notorious problems of the combinatorics of the [[axiom of determinacy]].
-Jackson earned his [[Ph.D.]] in [[1983]] at [[UCLA]] under the direction of [[Donald A. Martin]], with a [[dissertation]] on ''A Calculation of '''&delta;'''<sup>1</sup><sub>5</sub>.
+== References ==
-{{mathbio-stub}}
+{{Reflist}}
-[[Category:American mathematicians]]
-[[Category:20th century mathematicians]]
+== External links ==
-[[Category:21st century mathematicians]]
+* [http://www.math.unt.edu/~sjackson/some_papers.html List of papers published by Steve Jackson]
+* {{MathGenealogy|id=14679|name=Steve Jackson}}
+{{authority control}}
+{{DEFAULTSORT:Jackson, Steve}}
+[[Category:University of California, Los Angeles alumni]]
+[[Category:University of North Texas faculty]]
+[[Category:20th-century American mathematicians]]
+[[Category:21st-century American mathematicians]]
+[[Category:Living people]]
+[[Category:Year of birth missing (living people)]]
+[[Category:Set theorists]]
+{{US-mathematician-stub}}

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