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：我们构建了一个基于将语言片段合并为具有典范Henkin模型的理论的力迫框架。随后通过将其应用于扩展Namba问题及具有解释约束的特定理论（TCIs）模型分析，论证了该框架的实用性。在框架发展的同时，我们同步奠定了TCIs理论及其模型的基础，该基础研究本身亦具有独立价值。