Cohesive sets: countable and uncountable

Shore, Richard A.

doi:10.1090/S0002-9939-1974-0342382-X

Cohesive sets: countable and uncountable
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by Richard A. Shore PDF

Proc. Amer. Math. Soc. 44 (1974), 442-445 Request permission

Abstract:

We show that many uncountable admissible ordinals (including some cardinals) as well as all countable admissible ordinals have cohesive subsets. Exactly which cardinals have cohesive subsets, however, is shown to depend on set-theoretic assumptions such as $V = L$ or a large cardinal axiom.

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On splitting an $\alpha$-recursively enumerable set

The $\alpha$-recursively enumerable degrees are dense

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Admissible ordinals and recursion theory