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A NOTE ON INITIAL SEGMENTS OF THE ENUMERATION DEGREES
Published online by Cambridge University Press: 25 June 2014
Abstract
We show that no nontrivial principal ideal of the enumeration degrees is linearly ordered: in fact, below every nonzero enumeration degree one can embed every countable partial order. The result can be relativized above any total degree: if a,b are enumeration degrees, with a total, and a < b, then in the degree interval (a,b), one can embed every countable partial order.
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- Copyright © The Association for Symbolic Logic 2014
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