Independence results on the global structure of the Turing degrees

Authors:
Marcia J. Groszek and Theodore A. Slaman

Journal:
Trans. Amer. Math. Soc. **277** (1983), 579-588

MSC:
Primary 03D30; Secondary 03E35

DOI:
https://doi.org/10.1090/S0002-9947-1983-0694377-4

MathSciNet review:
694377

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Abstract | References | Similar Articles | Additional Information

Abstract: From CON(ZFC) we obtain: 1. CONZFC is arbitrarily large there is a locally finite upper semilattice of size which cannot be embedded into the Turing degrees as an upper semilattice).

2. CONZFC is arbitrarily large there is a maximal independent set of Turing degrees of size ).

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1983-0694377-4

Keywords:
Turing degrees,
forcing,
uncountable embeddings,
independent sets

Article copyright:
© Copyright 1983
American Mathematical Society