In this note we study several topics related to the schema of local reflection \(\textsf {Rfn} (T)\) and its partial and relativized variants. Firstly, we introduce the principle of uniform reflection with \(\varSigma _n\)-definable parameters, establish its relationship with relativized local reflection principles and corresponding versions of induction with definable parameters. Using this schema we give a new model-theoretic proof of the \(\varSigma _{n+2}\)-conservativity of uniform \(\varSigma _{n+1}\)-reflection over relativized local \(\varSigma _{n+1}\)-reflection. We also study the proof-theoretic strength of Feferman’s theorem, i.e., the assertion of 1-provability in S of the local reflection schema \(\textsf {Rfn} (S)\), and its generalized versions. We relate this assertion to the uniform \(\varSigma _2\)-reflection schema and, in particular, obtain an alternative axiomatization of \(\textsf {I} \varSigma _1\).

在本文中，我们研究了与局部反射\（\ textsf {Rfn}（T）\）及其部分和相对变体有关的主题。首先，我们介绍了具有（\ varSigma _n \）可定义参数的均匀反射原理，建立了它与相对论局部反射原理以及具有可定义参数的相应感应形式的关系。使用这种模式，我们给出了\（\ varSigma _ {n + 2} \）的新模型理论证明-均匀\（\ varSigma _ {n + 1} \）-相对论局部\（\ varSigma _ {n + 1} \）-反射。我们还研究了费弗曼定理的证明理论强度，即S中的1可证明性的断言本地反射模式\（\ textsf {Rfn}（S）\）及其广义版本。我们将此断言与统一的\（\ varSigma _2 \）-反射架构相关联，尤其是获得了\（\ textsf {I} \ varSigma _1 \）的替代公理化。