Undecidabiliity for the additive AIA fragment of the theory of normed spaces

Details Undecidabiliity for the additive AIA fragment of the theory of normed spaces Undecidabiliity for the additive AIA fragment of the theory of normed spaces

2010-02-06

arxiv.org/abs/1002.1381v2

Mathematics

Logic

12 pages, 2 figures, v2 corrects formatting errors

Scientific paper

An AIA formula is one of the form 'A implies B' where A and B are purely universal. Up to a simple reduction AIA formula are both EA and AE. In an earlier paper Solovay, Harrison and I proved the undecidability of validity for the AIA fragment of a two-sorted first-order language for normed vector spaces. In this note we find that validity remains undecidable for AIA sentences in the additive sublanguage, i.e., when multiplication is disallowed.

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