Constructing ﬡk-free structures

Given any fixed positive integer k and any R-algebra A with Aleph_k-free R-module structure we outline in the first part of the thesis a refined construction for arbitrarily large Aleph_k-free R-modules in ZFC with R-endomorphism algebra A. This will give an example of a more general construction method for Aleph_k-free structures combining the Easy Black Box with an ultra-strong Step-Lemma. In the second part of the thesis we apply this general construction method to the construction of arbitrarily large E(R)-algebras in ZFC with Aleph_k-free R-module structures.


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