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：我们发展了一种基于将语言片段融合为具有典范Henkin模型的理论的力迫框架。随后，通过将该框架应用于扩展的Namba问题以及具有解释约束的特定理论（TCIs）模型的分析，证明了该框架的实用性。在构建该框架的同时，我们并行奠定了TCIs及其模型的理论基础，这一基础本身具有独立研究价值。