Abstract Alongside the analogy between maximal ideals and complete theories, Jacobson radical carries over from of commutative rings to theories propositional calculi. This prompts a variant Lindenbaum’s Lemma that relates classical validity intuitionistic provability, syntactical counterpart which is Glivenko’s Theorem. The in fact turns out coincide with deductive closure. As by-product we ob...

The simulations were performed with two different models. Here too, a large part of the results was published earlier (in the various cited papers by Jacobson, Chen and Gettelman). In fact, the paper has strong overlap with Brasseur et al. (2016), Jacobson et al. (2013), and Chen and Gettelman (2016), even repeating some of the numerical values in the tables and one of the already published fig...