In this paper, we will prove that the plus cupping degrees generate a definable ideal on c.e. degrees different from other ones known so far, thus answering a question asked by Li and Yang (Proceedings of the 7th and the 8th Asian Logic Conferences. World Scientific Press, Singapore, 2003).

On definable filters in computably enumerable degrees.

The occasion of a retiring presidential address seems like a time to look back, take stock and perhaps look ahead.Institutionally, it was an honor to serve as President of the Association and I want to thank my teachers and predecessors for guidance and advice and my fellow officers and our publisher for their work and support. To all of the members who answered my calls to chair or serve on this or that committee, I offer my thanks as well. Your (...) work was both needed and appreciated.A major component of the efforts of the Association is devoted to our publications. My first important task as President was to deal with the need to reorganize the reviews section of the JSL and eventually to move it to the BSL. Appropriately enough, my first administrative job for the Association, some thirty years ago, was to serve on a committee to plan a reorganization of the reviews. I thank all those who helped with this transition and who took over the task of running the new reviews section. I hope that it will be another thirty years before further major changes are needed in this area and that someone else will be making them. (shrink)

Let [NB]₁ denote the ideal generated by nonbounding c.e. degrees and NCup the ideal of noncuppable c.e. degrees. We show that both [NB]₁ ∪ NCup and the ideal generated by nonbounding and noncuppable degrees are new, in the sense that they are different from M, [NB]₁ and NCup—the only three known definable ideals so far.

Let [NB]1 denote the ideal generated by nonbounding c.e. degrees and NCup the ideal of noncuppable c.e. degrees. We show that both [NB]1 ∩ NCup and the ideal generated by nonbounding and noncuppable degrees are new, in the sense that they are different from M, [NB]1 and NCup—the only three known definable ideals so far.