A nonlow2 R. E. Degree with the Extension of Embeddings Properties of a low2 Degree

Abstract

We construct a nonlow 2 r.e. degree d such that every extension of embedding property that holds below every low 2 degree holds below d. Indeed, we can also guarantee the converse so that there is a low r.e. degree c such that that the extension of embedding properties true below c are exactly the ones true below d. Moreover, we can also guarantee that no b ≤ d is the base of a nonsplitting pair.