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

作者：Goldbring Isaac^*

来源：Mathematical Logic Quarterly, 2012, 58(3): 208-216.

DOI：10.1002/malq.201110061

• Definable functions
• continuous logic
• Herbrand's theorem

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 absolutely ubiquitous structures from classical logic.

• 出版日期2012-5