Extending the intersection-with-submodels method to singular λi

Develop an extension of the intersection-with-submodels method that allows the parameters λi (i = 1,2,3,4) to be singular cardinals, thereby achieving Cichoń’s Maximum without large cardinals in the singular case.

Background

The method of intersection with submodels provides a way to force Cichoń’s Maximum without large cardinals, but as currently presented it handles only regular λi. In contrast, constructions via Boolean ultrapowers can treat singular λi.

The author explicitly notes a gap: adapting the intersection-with-submodels method to singular cardinal parameters is not yet known, pointing to a methodological open problem.