E. Todd Eisworth
Recent News
Education
Ph.D. University of Michigan
B.S. Louisiana State University
Professional Experience
2008-present Associate Professor, Ohio University
2013-2020 Chair, Department of Mathematics
2004-2008 Assistant Professor, Ohio University
2001-2004 Assistant Professor, University of Northern Iowa.
2000-2001 Visiting Assistant Professor, University of Northern Iowa
1999-2000 Visiting Assistant Professor, Ohio University
1997-1999 Post-doctoral researcher (under Saharon Shelah), Hebrew University of Jerusalem
1994-1997 Temporary Assistant Professor, University of Kansas
Awards
2007-2008 Grasselli Faculty Teaching Award, College of Arts and Sciences, Ohio University
2004 University Book and Supply Outstanding Teaching Award, University of Northern Iowa
1994 Sumner Myers Prize, University of Michigan
Research Interests
Dr. Eisworth’s research focuses on set theory and set-theoretic topology. He has particular interest in iterated forcing and combinatorial set theory.
Doctoral Students
Laura Dolph-Bosley (Ph.D. awarded 2009) Applications of elementary submodels in topology
Douglas Hoffman (Ph.D. awarded 2013) A coloring theorem for inaccessible cardinals
Frank Ballone (Ph.D. awarded 2017) -sets and the selection principle
Michael Perron (Ph.D. awarded 2017) On the structure of independent families
Shehzad Ahmed (Ph.D. awarded 2019) Progressive ideals in combinatorial set theory
Journal Publications (Current 2022)
Eisworth, T. (accepted) The pseudopower dichotomy, Journal of Symbolic Logic.
Eisworth, T. (in press) A note on the Revised GCH, Topology Appl.
Eisworth, T. (2022) Representability and compactness for pseudopowers, Archive for Mathematical Logic 61, no. 1-2, 55-80.
Dow, A. & Eisworth, T. (2015) CH and the Moore-Mrowka problem, Topology Appl. 195, 226-238.
Eisworth, T. (2014) On idealized versions of Pr_1, Archive for Mathematical Logic 53 no. 7-8, 809-824.
Eisworth, T. (2013) Getting more colors II, J. Symbolic Logic 78 No. 1 17-38.
Eisworth, T. (2013) Getting more colors I, J. Symbolic Logic 78 No. 1 1-16.
Eisworth, T. (2012) Simultaneous reflection and impossible ideals, J. Symbolic Logic 77 No. 4, 1325-1338.
Eisworth, T. (2010) Club guessing, stationary reflection, and coloring theorems, Annals of Pure and Applied Logic 161 1216-1243.
Eisworth, T. & Shelah, S. (2009) Successors of singular cardinals and coloring theorems II, J. Symbolic Logic 74 No. 4, 1287-1309.
Eisworth, T. & Nyikos, P. (2009) Antidiamond principles and topological applications, Trans. Amer. Math. Soc. 361, 5695-5719.
Eisworth, T. (2009) A note on strong negative partition relations, Fund. Math., 202, 97-123.
Eisworth, T. (2006) Elementary submodels and monotonically normal compacta, Topology Proceedings 30 No.2, 431-443.
Eisworth, T. (2006) Countable compactness, hereditary π-character, and the Continuum Hypothesis,
Topology and its Applications, 153 No. 18, 3572-3597.
Eisworth, T. & Nyikos, P. (2005) First countable, countably compact spaces and the Continuum Hypothesis, Transactions of the American Mathematical Society, 357, 4329-4347
Eisworth, T. & Shelah S. (2005) Successors of singular cardinals and coloring theorems I, Archive for Mathematical Logic, 44 no.5, 597-618.
- Balogh, T. Eisworth, G. Gruenhage, O. Pavlov, & P. Szeptycki (2004) Uniformization and anti-uniformization properties of ladder systems, Fundamenta Mathematicae, 181, 189-213.
Eisworth, T. (2003) On iterated forcing for successors of regular cardinals, Fundamenta Mathematicae 179 no. 3, 249-266.
Eisworth, T. (2003) A note on Jonsson cardinals, Topology Proceedings, 27 , no. 1, 173-178
Eisworth T., Nyikos P., & Shelah, S. (2003) Gently Killing S-spaces, T. Eisworth, P. Nyikos, and S. Shelah, Israel Journal of Mathematics, 136, 189-220.
Eisworth, T. (2002) PFA and perfect pre-images of , Topology and its Applications, 125, no. 2, 263-278.
Eisworth, T. (2002) Forcing and stable ordered-union ultrafilters, Journal of Symbolic Logic, 67 no. 1, 449-464.
Eisworth, T. (2001) Near coherence and filter games, T. Eisworth, Archive for Mathematical Logic 40 no. 3, 234-242.
Eisworth, T. (2001) CH and first countable, countably compact spaces, T. Eisworth, Topology and its Applications, 109 no. 1, 55-73.
Eisworth, T. (1999) Selective ultrafilters and , Proceedings of the American Mathematical Society 127 no. 10 3067-3071.
Eisworth, T. (1999) On countably compact spaces satisfying wD hereditarily, Topology Proceedings 24 (1999) Spring, 143-151.
Eisworth, T. & Roitman, J. (1999) CH with no Ostaszewski spaces, Transactions of the American Mathematical Society, 351 no. 7, 2675-2693.
Eisworth, T. and Nyikos, P. (1998) Recent applications of totally proper forcing, Topology Proceedings 23 339-348.
Book Chapters
Eisworth, T. (2010) Successors of Singular Cardinals. In Handbook of Set Theory, Matthew Foreman and Akihiro Kanamori eds., Chapter 15 1229-1350, Springer, 2010. ISBN 978-1-4020-4843-2.
Eisworth, T. (2007) On D-spaces. In Open Problems in Topology II, Elliott Pearl ed., Chapter 13, 129- 134, Elsevier Publishing, Amsterdam, The Netherlands, 2007. ISBN 0-444-52208-5.
Eisworth, T., Moore, J.T., & Milovich, D. (2013) Iterated forcing and the Continuum Hypothesis, In Appalachian Set Theory: 2006-2012, James Cummings and Ernest Schimmerling eds., Chapter 7 207-244, Cambridge University Press (London Mathematical Society Lecture Note Series v. 406) 2013. ISBN:9781107608504.
Invited Addresses and Workshops (current 2022)
What ELSE is PCF theory good for? New Directions in Set Theoretic Topology, University of Pittsburgh (workshop speaker) 2022
On and its relatives, Advances in Set Theory, Hebrew University of Jerusalem 2022
Representability and Pseudopowers, European Set Theory Conference, Vienna, Austria 2019
Sticks Above the Continuum, AMS Fall Central Sectional Meeting, Ann Arbor, MI 2018
On the Revised GCH, Special Conference on Set-Theoretic Topology, Auburn, AB 2017
What Can Independence Proofs Do For You?, 5th Annual Conference for the Exchange of Mathematical Ideas, Cedar Falls, IA 2017
Coloring Theorems and the Mahlo Hierarchy, AMS SE Regional meeting, Raleigh, NC 2016.
On λ-proper iterations, Independence results in mathematics and challenges in iterated forcing workshop, University of East Anglia, Norwich, UK 2015.
CH and the Moore-Mrowka Problem, 49th Spring Topology and Dynamics Conference, Bowling Green, OH 2015. (plenary)
CH and the Moore-Mrowka Problem, Alan Dow 60th Birthday Conference, Ithaca, NY 2014.
On the cov vs. pp problem, Fall Southeastern AMS sectional meeting, Louisville, KY 2013.
Higher cardinal characteristics and PCF, 20th BEST conference, Las Vegas, NV 2013 (plenary talk)
Complaints about Jonsson Cardinals, Workshop on iterated forcing and large cardinals, Toronto, 2012.
On Successors of Singular Cardinals, Winter School in Abstract Analysis, Czech Republic 2012 (three lecture workshop)
Coloring at successor of singulars, Logic Colloquium 2011, Barcelona, Spain 2011 (plenary)
Coloring at successor of singulars, BLAST 2011, Lawrence, KS. June 1-5, 2011. (plenary)
Coloring theorems at successors of singular cardinals, MAMLS Conference, Robert Morris University, Pittsburgh, PA, March 21, 2009. (plenary)
Iterated forcing and the Continuum Hypothesis, Appalachian Set Theory Workshop, Fields Institute, Toronto, ON, Canada. (with J. Moore: each speaker gave six 50 minute lectures over the course of two days)
Separable Monotonically Normal Compacta, Spring Topology and Dynamics Conference, University of Wisconsin, Milwaukee, Milwaukee WI, March 13-15 2008 (semi-plenary talk)
Some problems in combinatorial set theory, Workshop on Set Theory, Oberwolfach,Germany, January 14-18, 2008
Club-guessing and combinatorial set theory, Conference in honor of Andreas Blass’s 60th Birthday, The Fields Institute, Toronto ON, November 9-10, 2007
Club-guessing and combinatorial set theory, Special session on large cardinals in Set Theory, AMS Spring Sectional Meeting, Oxford, OH March 16- 17, 2007.
π-networks and closed pre-images of w1 , Spring Topology and Dynamics Conference, Rolla, MO March 29-31, 2007. (semi-plenary)
More consistency results with CH, Spring Topology and Dynamics Conference, Greensboro NC, March 23-25, 2006.
New Uses of Elementary Submodels, Summer Topology and Dynamics Conference, Granville OH, July 10-13, 2005. (plenary)
On square brackets partition relations, Spring Topology and Dynamics Conference, Rome GA, March 17-19, 2005.
Generalized Properness, Annual meeting of the ASL, Pittsburgh, PA, May 19-23, 2004.
On square brackets partition relations, Workshop on Singular Cardinal Combinatorics, BIRS Banff, AB Canada, May 1-6, 2004.
Forcing, CH, and the structure of topological spaces, International conference on logic and its applications in algebra and geometry, Ann Arbor, MI , April 11-13, 2003.
“I know it’s true, I just can’t prove it!”, MAA Iowa Section meeting, Cedar Falls, IA, April 4, 2003. (plenary address)
Iterated forcing “higher up”, Denison Topology Conference, Granville, OH, February 21-22, 2003. (one of 3 invited speakers)
Iterated forcing with uncountable supports, Zoltan Balogh Memorial Conference, Oxford, OH, November 15-16, 2002.
“This statement is false”, UNI Science Symposium, Cedar Falls, IA November 7, 2002 (keynote address)
What is a proof?, UNI Mathematics Conference, Cedar Falls, IA, September 2, 2002.
Remarks on Jonsson Cardinals, Boise Extravaganza in Set Theory, Boise, ID, March 29-31, 2002.
Coloring theorems at successors of singular cardinals, Spring Topology and Dynamics Conference, Austin, TX March 21-23 2002.
Cantor and the arithmetic of infinite sets, UNI Mathematics Conference, Cedar Falls, IA September 1, 2001.
Aspects of elementary submodels in topology, Summer Topology and Dynamics Conference, New York, NY July 18-21, 2001 (4 lecture workshop)
Countably tight perfect preimages of w1, Special session on set-theoretic topology, AMS spring sectional meeting, Lawrence, KS, March 30 – April 1, 2001.
CH and the Moore-Mrowka problem, Special session on set-theoretic topology, AMS fall sectional meeting, Toronto, ON Canada, September 23-24, 2000.
CH and the Moore-Mrowka problem, Summer Topology and Dynamics Conference, Oxford, OH July 26-29, 2000. (semi-plenary)
Applications of totally proper forcing in topology, Summer Topology and Dynamics Conference, Salt Lake City, UT, March 18-20, 1999. (semi-plenary)
Invited External Colloquia and Seminars
New Minimal Linear Orderings, Notre Dame Logic Seminar, October 4, 2022
Three Lectures on Totally Proper Forcing, Carolina Topology Seminar (virtual) Summer 2022.
The Revised GCH, Cornell Logic Seminar, Ithaca NY, September 2021.
Some new(?) useless(?) results in cardinal arithmetic, Carolina Topology Seminar, Charlotte (virtual), October 16, 2020.
Representability and Pseudopowers, Toronto Set Theory Seminar, Toronto (virtual) April 24, 2020.
An Introduction to cov vs. pp, Cornell Logic Seminar, Ithaca NY, 2019
A proof of cov vs. pp, Toronto Set Theory and Topology Seminar, Toronto, November 23, 2012.
On Jonsson Cardinals, Miami University Set Theory/Topology Seminar, Oxford, OH April 20, 2006.
Coloring Theorems, Carnegie-Mellon Mathematical Logic Seminar, Pittsburgh, PA, October 28, 2004.
CH and the Moore-Mrowka problem (2 lectures), University of Toronto Set Theory Seminar, Toronto, ON Canada, August 2-3, 2000.
CH, wD, and the Moore-Mrowka problem (2 lectures), University of Toronto Set Theory Seminar, Toronto, ON, Canada July 28 and August 4, 1999.
Gently Killing S-spaces, University of Toronto Set Theory Seminar, March 24, 1999
How Strong is the Continuum Hypothesis?, Mathematics Department Ohio University, Athens, OH. October 1998.
How Strong is the Continuum Hypothesis?, Mathematics Department University of South Carolina, Columbia, South Carolina, October 1997
Funded Grants
NSF Grant DMS 0506063 “Problems on Homogeneous Compacta” (co. PI with A. Arhangelskii) $147,963 2005-2007.
US-Israel Binational Science Foundation Grant No. 2002323 “Forcing for Set Theory of the Reals” (co-PI with A. Blass, A. Roslanowski, and S. Shelah) 2003-2006.