Archive for Mathematical Logic 49 (1):69-89 (2010)

We show the non-arithmeticity of 1st order theories of lattices of Σ n sentences modulo provable equivalence in a formal theory, of diagonalizable algebras of a wider class of arithmetic theories than has been previously known, and of the lattice of degrees of interpretability over PA. The first two results are applications of Nies’ theorem on the non-arithmeticity of the 1st order theory of the lattice of r.e. ideals on any effectively dense r.e. Boolean algebra. The theorem on degrees of interpretability relies on an adaptation of techniques leading to Nies’ theorem
Keywords Lattice of Σ n sentences  Diagonalizable algebra  Interpretability degrees  Arithmetic  Effectively inseparable Boolean algebra  Ideal definability
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Reprint years 2009, 2010
DOI 10.1007/s00153-009-0161-3
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References found in this work BETA

Model Theory.Wilfrid Hodges - 2008 - Stanford Encyclopedia of Philosophy.
Aspects of Incompleteness.Per Lindström - 1999 - Studia Logica 63 (3):438-439.
Undecidability in Diagonalizable Algebras.V. Yu Shavrukov - 1997 - Journal of Symbolic Logic 62 (1):79-116.
Recursion Theory.Anil Nerode & Richard A. Shore (eds.) - 1985 - American Mathematical Society.

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Citations of this work BETA

The∀∃ Theory of Peano Σ1 Sentences.Per Lindström & V. Yu Shavrukov - 2008 - Journal of Mathematical Logic 8 (2):251-280.
Interpretability Degrees of Finitely Axiomatized Sequential Theories.Albert Visser - 2014 - Archive for Mathematical Logic 53 (1-2):23-42.

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