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math.LO2011
An approximate Herbrand's theorem and definable functions in metric structures
Isaac Goldbring
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 af…
math.LO2010
Definable Operators on Hilbert Spaces
Isaac Goldbring
Let H be an infinite-dimensional (real or complex) Hilbert space, viewed as a metric structure in its natural signature. We characterize the definable linear operators on H as exac…