Faculty in Mathematics

Richard Ketchersid

Mathematician specializing in set theory and the foundations of mathematics. Ph.D. UC Berkeley, 2000 (advisor: W. Hugh Woodin).

Dr. Richard Ketchersid is a mathematician at Grand Canyon University whose research sits at the heart of modern set theory: descriptive set theory, determinacy, forcing, and the structure of L(ℝ) under AD+. He earned his Ph.D. at UC Berkeley in 2000 under W. Hugh Woodin, one of the most prominent set theorists of the past half-century, with a dissertation titled Toward ADR from the Continuum Hypothesis and an ω1-Dense Ideal.

His published work includes papers in the Journal of Symbolic Logic and the AMS Contemporary Mathematics series on stationary-tower forcing, Jónsson cardinals in L(ℝ), and Ramsey ultrafilters. He has frequent collaborators in Paul B. Larson (Miami University) and Jindřich Zapletal (University of Florida), with papers spanning 2006–2016 on forcing axioms and the combinatorics of countably-complete ultrafilters.

Before joining GCU, Dr. Ketchersid held positions at the University of Texas at Dallas, Miami University in Ohio, and the University of North Texas. At GCU he teaches MAT-144 College Mathematics and graduate-level mathematics coursework.

Research areas

  • Set theory
  • Descriptive set theory
  • Determinacy (AD, AD⁺, L(ℝ))
  • Forcing & large-cardinal combinatorics

Selected publications

  1. Jackson, S., Ketchersid, R., Schlutzenberg, F., Woodin, W. H. Determinacy and Jónsson cardinals in L(ℝ). Journal of Symbolic Logic, 2014. doi:10.1017/jsl.2014.49 ↗
  2. Caicedo, A. E., Ketchersid, R. A trichotomy theorem in natural models of AD+. Set Theory and Its Applications, AMS Contemporary Mathematics, vol. 533, 2011. doi:10.1090/conm/533/10510 ↗
  3. Ketchersid, R., Larson, P. B., Zapletal, J. Regular embeddings of the stationary tower and Woodin's Σ²₂ maximality theorem. Journal of Symbolic Logic, 2010. doi:10.2178/jsl/1268917500 ↗
  4. Ketchersid, R., Larson, P., Zapletal, J. Increasing δ¹₂ and Namba-style forcing. Journal of Symbolic Logic, 2007. doi:10.2178/jsl/1203350792 ↗
  5. Ketchersid, R., Larson, P., Zapletal, J. Ramsey ultrafilters and countable-to-one uniformization. Topology and Its Applications, vol. 213, 2016. Preprint (PDF) ↗

Education

2000

Ph.D., Mathematics

University of California, Berkeley

Dissertation: Toward ADR from the Continuum Hypothesis and an ω1-Dense Ideal. Advisor: W. Hugh Woodin.

Previous positions

  • The University of Texas at Dallas Senior Lecturer I
  • Miami University (Ohio) Visiting Assistant Professor
  • University of North Texas Faculty / postdoctoral