An approximate Herbrand's theorem and definable functions in metric structures

Details An approximate Herbrand's theorem and definable functions in metric structures An approximate Herbrand's theorem and definable functions in metric structures

2011-07-19

arxiv.org/abs/1107.3783v1

Mathematics

Logic

14 pages

Scientific paper

We develop a version of Herbrand's theorem for continuous logic and use it to prove that definable functions in infinite-dimensional Hilbert spaces are piecewise approximable by affine functions. We obtain similar results for definable functions in Hilbert spaces expanded by a group of generic unitary operators and Hilbert spaces expanded by a generic subspace. We also show how Herbrand's theorem can be used to characterize definable functions in some absolutely ubiquitous structures from classical logic.

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