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Correction to “Simple r. e. degree structures”

  • Robert S. Lubarsky (a1)

Extract

In the paper mentioned in the title (this Journal, vol. 52 (1987), pp. 208–213), it is shown that if ⊨ “V = HC is recursively inaccessible” is ω-standard -nonstandard, then = s.p.() has at most four r. e. degrees. They are 0 = deg(∅), = deg{eWe is a recursive well-ordering of ω}, = deg{R ⊨ “R codes a well-ordering”}, and . Furthermore, 0 < < and 0 < . Then it is claimed that < < and = if are each possible. In fact, < < always.

The mistake in the argument is that the model T is really a structure on a set, which we may as well take as ω: there is an Rω × ω, RT, and ‹ω, R› ≃ . So a copy of coded as a relation on ω is ≤ over . But there is no reason to think that the restriction of the isomorphism of and ‹ω, R› to is Σ1().

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