Hyperimmunity in 2\sp ℕ

Stephen Binns

doi:10.1305/ndjfl/1179323269

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Home > Journals > Notre Dame J. Formal Logic > Volume 48 > Issue 2 > Article

2007 Hyperimmunity in 2\sp ℕ

Stephen Binns

Notre Dame J. Formal Logic 48(2): 293-316 (2007). DOI: 10.1305/ndjfl/1179323269

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Abstract

We investigate the notion of hyperimmunity with respect to how it can be applied to Π{\sp 0}{\sb 1} classes and their Muchnik degrees. We show that hyperimmunity is a strong enough concept to prove the existence of Π{\sp 0}{\sb 1} classes with intermediate Muchnik degree—in contrast to Post's attempts to construct intermediate c.e. degrees.