Ken Kunen: Algebraist

Ken Kunen is justifiably best known for his work in set theory and topology. What I would guess many of his friends and students in those areas do not know is that Ken also did important work in algebra, especially in quasigroup and loop theory. In fact, I think it is not an exaggeration to say that his work in loop theory, both alone and in collaboration, revolutionized the field. In this paper, I would like to describe some of his accomplishments to nonspecialists. My point of view is personal, of course, and so I will give the most attention to those of his projects in which he collaborated with me. My hope is that the set theorists and topologists reading this will come away with an appreciation for what Ken was able to do in an area outside of his direct speciality. In the interest of space, I will have to leave out discussion of some of Ken’s work, such as his paper on alternative loop rings [15]. Ken’s approach to algebra utilized automated deduction tools and finite model builders. At the time most of what I am going to describe took place, the automated deduction software of choice was OTTER, developed by William McCune [18]. (McCune is best known to mathematicians for his solution to the Robbins Problem in Boolean algebras [20].) The finite model builder Ken used during the period I will discuss was SEM, developed by J. Zhang and H. Zhang [23]. In recent years, these have been supplanted by other tools, such as McCune’s Prover9, a successor to OTTER, and McCune’s model builder Mace4 [19].