A NOTE ON INITIAL SEGMENTS OF THE ENUMERATION DEGREES

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. t...

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Veröffentlicht in:	The Journal of symbolic logic 2014-06, Vol.79 (2), p.633-643
Hauptverfasser:	SLAMAN, THEODORE A., SORBI, ANDREA
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Sprache:	eng
Schlagworte:	Logic Mathematics Philosophy
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description	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.
doi_str_mv	10.1017/jsl.2013.1
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source	JSTOR Mathematics & Statistics; Jstor Complete Legacy; Cambridge University Press Journals Complete
subjects	Logic Mathematics Philosophy
title	A NOTE ON INITIAL SEGMENTS OF THE ENUMERATION DEGREES
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