Publications

A summary of my research is available (PDF format).

Research papers

  • “On the existence of a connected component of a graph”, Kirill Gura, Jeffry L. Hirst, and Carl Mummert. Preprint: arXiv:1406.4786
  • “The modal logic of Reverse Mathematics”, Carl Mummert, Alaeddine Saadaoui, and Sean Sovine. To appear, Archive for Mathematical Logic. Preprint: arXiv:abs/1401.0648
  • “Reverse mathematics and properties of finite character”, Damir D. Dzhafarov and Carl Mummert. Annals of Pure and Applied Logic, v. 163, 2012, pp. 1243–1251. DOI 10.1016/j.apal.2012.01.007. Preprint: arXiv:1109.3378
  • “On the strength of the finite intersection principle”, Damir D. Dzhafarov and Carl Mummert. Israel Journal of Mathematics, v. 191, 2012, pp. 1–17. DOI 10.1007/s11856-012-0150-9. Preprint: arXiv:1109.3374
  • “Reverse mathematics and uniformity in proofs without excluded middle”, Jeffry L. Hirst and Carl Mummert, Notre Dame Journal of Formal Logic v. 52, 2011, pp. 149–162. DOI 10.1215/00294527-1306163. Preprint: arXiv:1010.5165
  • “Stationary and convergent strategies in Choquet games”, François G. Dorais and Carl Mummert, Fundamenta Mathematicae v. 209, 2010, pp. 59–79. DOI 10.4064/fm209-1-5. Preprint: arXiv:0907.4126
  • “Topological aspects of poset spaces”, Carl Mummert and Frank Stephan, Michigan Mathematical Journal v. 59, 2010, pp. 3–24. DOI 10.1307/mmj/1272376025. Preprint: arXiv:0912.3191
  • “Subsystems of second-order arithmetic between WKL0 and RCA0“, Archive for Mathematical Logic v. 47 n. 3, 2008, pp. 205–210. DOI 10.1007/s00153-008-0074-6. Preprint: ps pdf
  • “Reverse mathematics of MF spaces”, Journal of Mathematical Logic v. 6 n. 2, 2007, pp. 203–232. DOI 10.1142/S0219061306000578. Preprint: ps pdf
  • “Filters on computable posets”, Steffen Lempp and Carl Mummert, Notre Dame Journal of Formal Logic v. 47 n. 4, 2006, pp. 479–485. DOI 10.1305/ndjfl/1168352662. Preprint: ps pdf
  • “Reverse Mathematics and Π12 comprehension”, Carl Mummert and Stephen G. Simpson, Bulletin of Symbolic Logic v. 11 n. 4, 2005, pp. 526–533. DOI 10.2178/bsl/1130335208. Preprint: ps pdf
  • “An incompleteness theorem for βn models”, Carl Mummert and Stephen G. Simpson, Journal of Symbolic Logic v. 29 n. 2, 2004, pp. 612–616. DOI 10.2178/jsl/1082418545. Preprint: ps pdf

Books

  • Reverse Mathematics, Damir D. Dzhafarov and Carl Mummert, Theory and Applications of Computability, CIE/Springer. In preparation.
  • Finite Fields and Applications, Gary Mullen and Carl Mummert, AMS Student Mathematical Library v. 41, 2007. 175 pages. ISBN: 978-0-8218-4418-2. Amazon.com sales page

Dissertation

  • On the Reverse Mathematics of General Topology. PhD thesis, Penn State, 2005. Download: pdf

Author identifiers

My ORCID id is orcid.org/0000-0002-8290-9458. My arXiv id is
au:Mummert_C.