Richard L.Kramer

Department of Mathematics
Iowa State University

Office: 376 Carver

Unpublished Manuscripts:

[1] Definability in the foundations of geometry and the product rule for derivations. This paper is from a conference talk that I gave in Bogotá, Colombia at Universidad de los Andes, as part of the Model Theory in Bogotá (Summer 2005) conference. It summarises the work (much of it unpublished) that I have done in the Foundations of Goemetry and some related algebraic results motivated by this research.

[2] The product rule for derivations on finite dimensional split semi-simple Lie algebras over a field of characteristic zero

[3] The classical Ramsey number R(3,3,3,3) is no greater than 62 This is an updated version of my original 1996 manuscript proving what is still the best known upper bound for the classical ramsey number R(3,3,3,3). The results of this paper were the subject of a semester long series of talks given in the Graph Theory seminar at Iowa State University during the spring semester of 1994.

Submitted for Publication:

[1] The classical Ramsey number R(3,3,3,3) is no greater than 62: The global arguements

Publications in Print:

[1] An upper bound of 62 on the classical Ramsey number R (3,3,3,3), (with S. Fettes and S. Radziszowski), Ars. Combinatorica, LXXII (2004), pp. 41-63, MR 2005f:05105 Zbl pre02192105.

[2] The periodic Hopf ring of connective Morava K- theory, (with J. Boardman and W. S. Wilson), Forum Mathematicum 11 (1999), pp. 761-766, MR 2004k:55009, Zbl 0930.55002.

[3] Total tense algebras and symmetric semisimple relation algebras, (with P. Jipsen and R. Maddux), Algebra Universalis 43 (1995), pp. 402-423, MR 96h:03104, Zbl 0836.08004.

[4] The undefinability of intersection from perpendicularity in the 3-dimensional Euclideanm geometry of lines, Geometriea Dedicada 46 (1993), pp. 207-210, MR 94a:51029, Zbl 0778.51007.

[5] Relativized relation algebras, Proceedings of the Conference on Algebraic Logic, Budapest, Hungary (1991), pp. 293-349, MR 93c:03081, Zbl 749.03047.

[6] A simple proof of the subgroup theorem for free groups, (with A. Abian), Bull. Math. De la Soc. Sci. Math. De la R. S. Roumanie 28 (1984), pp. 3- 12, MR 85i:20030, Zbl 0543.20019.

[7] Equations not preserved under complete extentions, (with R. Maddux), Algebra Universalis 15 (1982), pp. 86-89 MR 83i:03098, Zbl 552.03054.

[8] Hierarchies of sets and degrees below 0', (with R. Epstein and R. Hass), Proceedings, Logic Year 1979-80, The University of Connecticut, Lecture Notes in Mathematics 859 Springer-Verlag, (1981), pp. 32-48. MR 82k:03073, Zbl 0467.03046.

Below are the two good (that is, monochromatic triangle free) edge colorings on the complete graph with 16 vertices using 3 colors, unique up to isomorphism. Their existence proves the lower bound of the classical Ramser number R(3,3,3)=17. My own work in this field involves the upper bound for the corresponding 4 color number R(3,3,3,3).