Splittings of 0' into the Recursively Enumerable Degrees | Zendy

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Splittings of 0' into the Recursively Enumerable Degrees

Author(s) -

Yi Xiaoding

Publication year - 1996

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/malq.19960420122

Subject(s) - recursively enumerable language , mathematics , degree (music) , combinatorics , existential quantification , maximal set , dual (grammatical number) , discrete mathematics , mathematics subject classification , subject (documents) , computer science , set (abstract data type) , physics , art , literature , programming language , library science , acoustics

Lachlan [9] proved that there exists a non‐recursive recursively enumerable (r. e.) degree such that every non‐recursive r. e. degree below it bounds a minimal pair. In this paper we first prove the dual of this fact. Second, we answer a question of Jockusch by showing that there exists a pair of incomplete r. e. degrees a 0 , a 1 such that for every non‐recursive r. e. degree w , there is a pair of incomparable r. e. degrees b 0 , b 2 such that w = b 0 V b 1 and b i for i = 0, 1. Mathematics Subject Classification: 03D25, 03D30.

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