We develop a forcing framework based on the idea of amalgamating language fragments into a theory with a canonical Henkin model. We then demonstrate the usefulness of this framework by applying it to both the extended Namba problem and the analysis of models of certain theories with constraints in interpretation (TCIs). The foundations for a theory of TCIs and their models are laid in parallel to the development of our framework, and are of independent interest.

翻译：我们发展了一个基于语言片段融合至具有典范Henkin模型的理论的力迫框架。随后，通过将该框架应用于扩展Namba问题以及特定解释约束理论（TCIs）模型的解析，我们展示了其应用价值。在框架构建过程中，我们的理论基础与TCIs及其模型的构建同步推进，且这一理论具有独立的研究价值。