# Richard L.Kramer

##
Lecturer

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## Unpublished Manuscripts: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unpublished) that I have done in the Foundations of Goemetry and some related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).