•  22
    A nonlow2 R. E. Degree with the Extension of Embeddings Properties of a low2 Degree
    with R. A. Shore
    Mathematical Logic Quarterly 48 (1): 131-146. 2002.
    We construct a nonlow2 r.e. degree d such that every positive extension of embeddings property that holds below every low2 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 embeddings properties true below c are exactly the ones true belowd.Moreover, we can also guarantee that no b ≤ d is the base of a nonsplitting pair
  •  44
    The minimal e-degree problem in fragments of Peano arithmetic
    with M. M. Arslanov, C. T. Chong, and S. B. Cooper
    Annals of Pure and Applied Logic 131 (1-3): 159-175. 2005.
    We study the minimal enumeration degree problem in models of fragments of Peano arithmetic () and prove the following results: in any model M of Σ2 induction, there is a minimal enumeration degree if and only if M is a nonstandard model. Furthermore, any cut in such a model has minimal e-degree. By contrast, this phenomenon fails in the absence of Σ2 induction. In fact, whether every Σ2 cut has minimal e-degree is independent of the Σ2 bounding principle