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A nonlow 2 R. E. Degree with the Extension of Embeddings Properties of a low 2 Degree
Author(s) -
Shore Richard A.,
Yang Yue
Publication year - 2002
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/1521-3870(200201)48:1<131::aid-malq131>3.0.co;2-z
Subject(s) - degree (music) , converse , mathematics , extension (predicate logic) , base (topology) , construct (python library) , combinatorics , discrete mathematics , mathematical analysis , computer science , geometry , physics , acoustics , programming language
We construct a nonlow 2 r.e. degree d such that every positive extension of embeddings 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 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.