Stephen C. Jackson

Previous Scheduled Teaching

Published Intellectual Contributions

Abstracts and Proceedings

• with R. D. Mauldin. (2002). Sets Meeting Isometric Copies of the lattice Z2 In Exactly one Point.

Book Chapter

• Jackson, S.C. (2018). Towards a Theory of Definable Sets. Proceedings to the International Congress of Mathematicians 2018. 1 25-44.
• Jackson, S. (2012). Projective ordinals. Introduction to Part IV. Wadge degrees and projective ordinals. The Cabal Seminar. Volume II. 37 199--269. Assoc. Symbol. Logic, La Jolla, CA.
• Jackson, S. (2012). Regular cardinals without the weak partition property. Wadge degrees and projective ordinals. The Cabal Seminar. Volume II. 37 509--517. Assoc. Symbol. Logic, La Jolla, CA.
• Jackson, S. (2010). Cardinal structure under AD. Logic Colloquium 2007. 35 92--131. Assoc. Symbol. Logic, La Jolla, CA.
• Jackson, S. (2010). Structural consequences of AD. Handbook of set theory. Vols. 1, 2, 3. 1753--1876. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5764-9_22
• Jackson, S. (2008). Suslin cardinals, partition properties, homogeneity. Introduction to Part II. Games, scales, and Suslin cardinals. The Cabal Seminar. Vol. I. 31 273--313. Assoc. Symbol. Logic, Chicago, IL. https://doi.org/10.1017/CBO9780511546488.015
• Boykin, C.M., Jackson, S. (2007). Borel boundedness and the lattice rounding property. Advances in logic. 425 113--126. Amer. Math. Soc., Providence, RI. https://doi.org/10.1090/conm/425/08121
• Boykin, C.M., Jackson, S. (2006). Some applications of regular markers. Logic Colloquium '03. 24 38--55. Assoc. Symbol. Logic, La Jolla, CA.
• Jackson, S. (1992). Admissibility and Mahloness in $L({\bf R})$. Set theory of the continuum (Berkeley, CA, 1989). 26 63--74. Springer, New York. https://doi.org/10.1007/978-1-4613-9754-0_5
• Jackson, S. (1988). ${\rm AD}$ and the projective ordinals. Cabal Seminar 81--85. 1333 117--220. Springer, Berlin. https://doi.org/10.1007/BFb0084974
• Jackson, S., Martin, D.A. (1983). Pointclasses and well-ordered unions. Cabal seminar 79--81. 1019 56--66. Springer, Berlin. https://doi.org/10.1007/BFb0071693

Conference Proceeding

• S. Gao, S. Jackson, and Y. Zhang, eds.. (2007). Advances in Logic. The North Texas Logic Conference, October 8-10, 2004, University of North Texas, Denton. Contemporary Mathematics. Providence, RI, American Mathematical Society.

Journal Article

• Allaart, P.C., Jackson, S.C., Jones, R.T., Lambert, D. (2023). On the existence of numbers with matching continued fraction and decimal expansions. Monatshefte für Mathematik. 202 (1) 1-30.
• Trang, N., Jackson, S.C., Chan, W. (2023). More definable combinatorics around the first and second uncountable cardinal. Journal of Mathematical Logic. 23 (03) World Scientific.
• Jackson, S.C., Conley, C., Marks, A., Seward, B., Tucker-Drob, R. (2023). Borel Asymptotic Dimension and Hyperfinite Equivalence Relations. Duke Mathematical Journal. 176 (16) 3175-3226.
• Jackson, S.C., Creiner, A. (2023). Borel Complexity and Ramsey Largeness of Sets of Oracles Separating Complexity Classes. Mathematical Logic Quarterly. 63 (3) 267-286.
• Fishman, L., Jackson, S.C., Crone, L. (2022). Equivalence Relations and Determinacy. Journal of Mathematical Logic. 22 (1) 19.
• Jackson, S.C., Mance, W., Roth, S. (2022). A Non-Borel Special Alpha Limit Set in the Plane. Ergodic Theory and Dynamical Systems. 42 (8) 2550-2560.
• Fishman, L., Crone, L., Jackson, S.C. (2022). DETERMINACY OF SCHMIDT’S GAME AND OTHER INTERSECTION GAMES. The Journal of Symbolic Logic.
• Fishman, L., Jackson, S.C., Crone, L. (2022). Hausdorff Dimension Regularity Properties and Games. Israel Journal of Mathematics. 248 (481–500)
• Jackson, S.C., Chan, W. (2021). Definable Combinatorics at the First Uncountable Cardinal. Transactions of the American Mathematical Society. 374 (3) 2035-2056.
• Trang, N., Jackson, S.C., Chan, W. (2021). The size of the class of countable sequences of ordinals. Transactions of the American Mathematical Society. https://www.ams.org/journals/tran/0000-000-00/S0002-9947-2021-08573-6/
• Jackson, S.C., Crone, L., Fishman, L. Equivalence Relations and Determinacy. Journal of Mathematical Logic. 22 (1) 19.
• Jackson, S.C., Chan, W. (2021). The destruction of the Axiom of Determinacy by forcings on R when Theta is regular.. Israel Journal of Mathematics. 241 119-138.
• Jackson, S.C., Airey, D., Mance, W. (2020). Some Complexity Results in the Theory of Normal Numbers. Canadian Journal of Mathematics. 1-29.
• Jackson, S.C., Airey, D., Mance, W. Descriptive Complexity in Cantor Series. Journal of Symbolic Logic.
• Fishman, L., Crone, L., Hiers, N., Jackson, S.C. (2019). EQUIVALENCE OF THE ROTHBERGER AND 2-ROTHBERGER GAMES FOR HAUSDORFF SPACES. Topology and its Applications. 258 172-176.
• Jackson, S.C., Conley, C., Marks, A., Seward, B., Tucker-Drob, R. Hyperfiniteness and Borel combinatorics. Journal of the European Mathematical Society. 22 (3) 877-892.
• Jackson, S.C., Chan, W. (2019). L(R) with Determinacy Satisfies the Suslin Hypothesis. Advances in Mathematics. 346 305-328. Elsevier.
• Conley, C.T., Jackson, S.C., Kerr, D., Marks, A.S., Seward, B., Tucker-Drob, R.D. (2018). F\o lner tilings for actions of amenable groups. Other. 371 (1-2) 663--683. https://doi.org/10.1007/s00208-017-1633-0
• Henkis, D., Jackson, S., Lobe, J. (2017). Restricted Steinhaus sets in the plane. Other. 238 (2) 153--166. https://doi.org/10.4064/fm260-7-2016
• Jackson, S., Khafizov, F.T. (2016). Descriptions and cardinals below $\delta_5^1$. Other. 81 (4) 1177--1224. https://doi.org/10.1017/jsl.2016.7
• Henkis, D., Jackson, S., Lobe, J. (2016). The finite Steinhaus problem. Other. 67 (4) 551--564.
• Backs, K., Jackson, S., Mauldin, R.D. (2015). CH, $\bold V=\bold L$, disintegration of measures, and $\Pi_1^1$ sets. Other. 274 76--96. https://doi.org/10.1016/j.aim.2014.12.011
• Gao, S., Jackson, S. (2015). Countable abelian group actions and hyperfinite equivalence relations. Inventiones Mathematicae. 201 (1) 309-383.
• Jackson, S.C., Ketchersid, R., Schlutzenberg, F., Woodin, W.H. (2014). Determinacy and J\'onsson cardinals in $L(\Bbb R)$. Other. 79 (4) 1184--1198. https://doi.org/10.1017/jsl.2014.49
• Jackson, S., L\"owe, Benedikt. (2013). Canonical measure assignments. Other. 78 (2) 403--424. http://projecteuclid.org/euclid.jsl/1368627057
• Apter, A.W., Jackson, S.C., L\"owe, Benedikt. (2013). Cofinality and measurability of the first three uncountable cardinals. Other. 365 (1) 59--98. https://doi.org/10.1090/S0002-9947-2012-05497-3
• S. Gao, S. Jackson, and B. Sari. (2011). On the complexity of the uniform homeomorphism relation between separable Banach spaces. Transactions of the American Mathematical Society. 363 (6) 3071-3099.
• Gao, S., Jackson, S.C., Sari, B. (2011). On the complexity of the uniform homeomorphism relation between separable Banach spaces. Transactions of the American Mathematical Society. 363 (6) 3071-3099.
• S. Gao, S. Jackson, and V. Kieftenbeld. (2010). The Laczkovich-Komjath property for coanalytic equivalence relations. The Journal of Symbolic Logic. 75 (3) 1091-1101.
• S. Gao, S. Jackson, and B. Seward. (2009). A coloring property for countable groups. Mathematical Proceedings of the Cambridge Philosophical Society. 147 (3) 579-592.
• S. Gao, S. Jackson, and V. Kieftenbeld. (2008). A classification of ordinals up to Borel isomorphism. Fundamenta Mathematicae. 198 61-76.
• S. Gao, S. Jackson, M. Laczkovich, and R. D. Mauldin. (2008). On unique representation of families of sets. Transactions of the American Mathematical Society. 360 (2) 939-958.
• Jackson, S.C. (2008). Suslin Cardinals, Partition Properties, and Homogeneity.
• Jackson, S., May, R. (2004). The strong partition relation on $\omega_1$ revisited. Other. 50 (1) 33--40. https://doi.org/10.1002/malq.200310073
• Jackson, S., Mauldin, R.D. (2003). Survey of the Steinhaus tiling problem. Other. 9 (3) 335--361. https://doi.org/10.2178/bsl/1058448676
• Jackson, S.C., Kechris, A.S., Louveau, A. (2002). Countable Borel equivalence relations. Other. 2 (1) 1--80. https://doi.org/10.1142/S0219061302000138
• Freiling, C., Jackson, S. (2002). Infinite block maps and generalized Bernoulli measures. Other. (26th Summer Symposium Conference, suppl.) 11--34.
• Jackson, S., Mauldin, R.D. (2002). On a lattice problem of H. Steinhaus. Other. 15 (4) 817--856. https://doi.org/10.1090/S0894-0347-02-00400-9
• Jackson, S., Mauldin, R.D. (2002). Sets meeting isometric copies of the lattice ${\bf Z}^2$ in exactly one point. Other. 99 (25) 15883--15887. https://doi.org/10.1073/pnas.222551699
• Becker, H., Jackson, S. (2001). Supercompactness within the projective hierarchy. Other. 66 (2) 658--672. https://doi.org/10.2307/2695035
• Jackson, S. (2001). The weak square property. Other. 66 (2) 640--657. https://doi.org/10.2307/2695034
• Apter, A.W., Henle, J.M., Jackson, S.C. (2000). The calculus of partition sequences, changing cofinalities, and a question of Woodin. Other. 352 (3) 969--1003. https://doi.org/10.1090/S0002-9947-99-02554-4
• Jackson, S. (1999). A computation of $\delta^1_5$. Other. 140 (670) viii+94. https://doi.org/10.1090/memo/0670
• Jackson, S., Mauldin, R.D. (1999). On the $\sigma$-class generated by open balls. Other. 127 (1) 99--108. https://doi.org/10.1017/S0305004199003552
• Erd\Hos, P., Jackson, S., Mauldin, R.D. (1997). On infinite partitions of lines and space. Other. 152 (1) 75--95.
• Jackson, S.C., Zamboni, L.Q. (1995). A note on a theorem of Chiswell. Other. 123 (9) 2629--2631. https://doi.org/10.2307/2160553
• Jackson, S., Mauldin, R.D. (1994). Borel measurable selections of Paretian utility functions. Other. 23 (4) 361--378. https://doi.org/10.1016/0304-4068(94)90019-1
• Erd\Hos, P., Jackson, S., Mauldin, R.D. (1994). On partitions of lines and space. Other. 145 (2) 101--119.
• Brand, N., Jackson, S. (1994). Properties of classes of random graphs. Other. 3 (4) 435--454. https://doi.org/10.1017/S0963548300001346
• Dougherty, R., Jackson, S.C., Kechris, A.S. (1994). The structure of hyperfinite Borel equivalence relations. Other. 341 (1) 193--225. https://doi.org/10.2307/2154620
• Jackson, S., Mauldin, R.D. (1992). Some complexity results in topology and analysis. Other. 141 (1) 75--83. https://doi.org/10.4064/fm-141-1-75-83
• Jackson, S. (1991). Admissible Suslin cardinals in $L({\bf R})$. Other. 56 (1) 260--275. https://doi.org/10.2307/2274918
• Jackson, S., Mauldin, R.D. (1991). Nonuniformization results for the projective hierarchy. Other. 56 (2) 742--748. https://doi.org/10.2307/2274715
• Jackson, S. (1990). A new proof of the strong partition relation on $\omega_1$. Other. 320 (2) 737--745. https://doi.org/10.2307/2001700
• Jackson, S. (1990). An unboundedness property for norms of length $\geq \omega_2$. Other. 109 (2) 487--491. https://doi.org/10.2307/2048012
• Jackson, S. (1990). Partition properties and well-ordered sequences. Other. 48 (1) 81--101. https://doi.org/10.1016/0168-0072(90)90081-C
• Jackson, S. (1989). AD and the very fine structure of $L({\bf R})$. Other. 21 (1) 77--81. https://doi.org/10.1090/S0273-0979-1989-15766-2

Monograph

• Gao, S., Seward, B., Jackson, S.C. (2016). Group colorings and Bernoulli subflows. Memoirs of the American Mathematical Society. 241 (1141) vi+241pp.

Popular Press Article

• Jackson, S.C. (1989). Bulletin Announcement: AD and the Projective Ordinals.

Scholarly Note

• Jackson, S.C., Martin, D.A. (2022). Kunen's work on Determinacy and Descriptive Set Theory (Notices of the AMS). Notices of the American Mathematical Society. 69 (10) 1763-1765.

Contracts, Grants and Sponsored Research

Grant - Research

• Jackson, S.C., Gao, S., "Descriptive Dynamics and Borel Combinatorics of Group Actions," sponsored by National Science Foundation, Federal, $270000 Funded. (2018 - 2022).
• Urbanski, M. (Co-Principal), Gao, S. (Principal), , D. (Co-Principal), Jackson, S.C. (Co-Principal), "Research Training Group in Logic and Dynamics [NSF]," sponsored by UNT, Federal, $1500000 Funded. (2010 - 2016).
• Jackson, S.C. (Co-Principal), Gao, S. (Principal), "Descriptive Dynamics and Borel Combinatorics of Group Actions," sponsored by National Science Foundation, FED, Funded. (2018 - 2022).
• Urbanski, M. (Principal), Mauldin, R.D. (Co-Principal), Jackson, S.C. (Principal), Gao, S. (Principal), "Research Training Group in Logic and Dynamics," sponsored by National Science Foundation, FED, Funded. (2010 - 2016).
• Jackson, S.C. (Co-Principal), Gao, S. (Principal), "Equivalence Relations, Symbolic Dynamics and Descriptive Set Theory," sponsored by National Science Foundation, FED, Funded. (2012 - 2016).