Relatively recursive expansions
Ash, C. ; Knight, J.
Fundamenta Mathematicae, Tome 141 (1992), p. 137-155 / Harvested from The Polish Digital Mathematics Library
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In this paper, we consider the following basic question. Let A be an L-structure and let ψ be an infinitary sentence in the language L∪R, where R is a new relation symbol. When is it the case that for every B ≅ A, there is a relation R such that (B,R) ⊨ ψ and R≤TD(B)? We succeed in giving necessary and sufficient conditions in the case where ψ is a “recursive” infinitary Π2 sentence. (A recursive infinitary formula is an infinitary formula with recursive disjunctions and conjunctions.) We consider also some variants of the basic question, in which R is r.e., Δα0, or Σα instead of recursive relative to D(B).

Publié le : 1992-01-01
EUDML-ID : urn:eudml:doc:211934 
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Ash, C.; Knight, J. Relatively recursive expansions. Fundamenta Mathematicae, Tome 141 (1992) pp. 137-155. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv140i2p137bwm/

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