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  1. The Ricean Objection: An Analogue of Rice's Theorem for First-Order Theories.Igor Oliveira & Walter Carnielli - 2008 - Logic Journal of the IGPL 16 (6):585-590.
    We propose here an extension of Rice's Theorem to first-order logic, proven by totally elementary means. If P is any property defined over the collection of all first-order theories and P is non-trivial over the set of finitely axiomatizable theories , then P is undecidable. This not only means that the problem of deciding properties of first-order theories is as hard as the problem of deciding properties about languages accepted by Turing machines, but also offers a general setting for proving (...)
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  • Index Sets for Π01 Classes.Douglas Cenzer & Jeffrey Remmel - 1998 - Annals of Pure and Applied Logic 93 (1-3):3-61.
    A Π01 class is an effectively closed set of reals. We study properties of these classes determined by cardinality, measure and category as well as by the complexity of the members of a class P. Given an effective enumeration {Pe:e < ω} of the Π01 classes, the index set I for a certain property is the set of indices e such that Pe has the property. For example, the index set of binary Π01 classes of positive measure is Σ02 complete. (...)
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  • Index Sets for< I> Π_< Sup> 0< Sub> 1 Classes.Douglas Cenzer & Jeffrey Remmel - 1998 - Annals of Pure and Applied Logic 93 (1):3-61.
  • Representations of the Real Numbers and of the Open Subsets of the Set of Real Numbers.Klaus Weihrauch & Christoph Kreitz - 1987 - Annals of Pure and Applied Logic 35 (3):247-260.