Degrees of recursively saturated models

Authors:
Angus Macintyre and David Marker

Journal:
Trans. Amer. Math. Soc. **282** (1984), 539-554

MSC:
Primary 03D45; Secondary 03C50, 03C57, 03C62, 03H15

MathSciNet review:
732105

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Abstract: Using relativizations of results of Goncharov and Peretyat'kin on decidable homogeneous models, we prove that if is -saturated for some Scott set , and is an enumeration of , then has a presentation recursive in . Applying this result we are able to classify degrees coding (i) the reducts of models of PA to addition or multiplication, (ii) internally finite initial segments and (iii) nonstandard residue fields. We also use our results to simplify Solovay's characterization of degrees coding nonstandard models of Th(**N**).

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1984-0732105-5

Keywords:
Scott set,
Turing degree,
recursively saturated model,
model of arithmetic

Article copyright:
© Copyright 1984
American Mathematical Society