论文标题
贝丝确定性和石材 - 韦尔斯特拉斯定理
Beth definability and the Stone-Weierstrass Theorem
论文作者
论文摘要
紧凑型Hausdorff空间的Stone-Weierstrass定理是功能分析的基本结果，其影响深远。我们引入了与无限品种$δ$相关的方程逻辑$ \vdash_Δ$，并表明Stone-WeierStrass定理是$ \vdash_Δ$的Beth Distarability属性的结果，并指出每个隐性定义都可以显式。此外，我们通过希尔伯特风格的微积分来定义一个无限的命题逻辑$ \vdash_δ$，并证明了与$ \vdash_δ$相关的后果的语义概念，与$ \vdash_δ$相吻合。
The Stone-Weierstrass Theorem for compact Hausdorff spaces is a basic result of functional analysis with far-reaching consequences. We introduce an equational logic $\vDash_Δ$ associated with an infinitary variety $Δ$ and show that the Stone-Weierstrass Theorem is a consequence of the Beth definability property of $\vDash_Δ$, stating that every implicit definition can be made explicit. Further, we define an infinitary propositional logic $\vdash_Δ$ by means of a Hilbert-style calculus and prove a strong completeness result whereby the semantic notion of consequence associated with $\vdash_Δ$ coincides with $\vDash_Δ$.
