Continuum hypothesis as a model-theoretical problem

CH is approached as a problem about the cardinality of the second number class $\Gamma$. For the purpose, the theory of constituents is extended to the countably infinite case where the nodes of a constituent tree are sequences of finite constituents. Certain branches (‘perfect’ ones) specify the structures of which a model of a countably infinite constituent consists. In the case of $\Gamma$, these branches keep on splitting indefinitely and hence have the cardinality of the continuum. Since $\Gamma$ is maximal, they are all satisfied in it.