一个近似Herbrand定理与度量结构中的可定义函数
An approximate Herbrand's theorem and definable functions in metric structures
摘要：
我们开发了一个版本的赫布兰德定理连续逻辑和使用它来证明，可定义的功能在无限维希尔伯特空间分段逼近仿射函数。对于由一般酉算子展开的Hilbert空间和由一般子空间展开的希尔伯特空间中的可定义函数，我们得到了类似的结果.我们还展示了如何Herbrand的定理可以用来描述一些绝对无处不在的结构，从经典逻辑中的可定义的功能。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
