There is no plus-capping degree

Summary Answering a question of Per Lindström, we show that there is no plus-capping degree, i.e. that for any incomplete r.e. degreew, there is an incomplete r.e. degreea>w such that there is no r.e. degreev>w withav=w.Mathematics subject classification: 03D30The authors would like to thank Per Lindström for raising the question and Carl Jockusch for communicating it to them. The first author was partially supported by a U.S./New Zealand binational grant. The second author was partially supported by NSF grant DMS-9100114 and the U.S./New Zealand binational NSF grant INT-9020558