Near coherence of filters. III: A simplified consistency proof (Q914666)

[For Parts I, II by the first author see, respectively, Notre Dame J. Formal Logic 27, 579-591 (1986; Zbl 0622.03040) and Trans. Am. Math. Soc. 300, 557-581 (1987; Zbl 0647.03043).] This paper gives a new proof of the consistency with ZFC of the principle of Near Coherence of Filters, already proved in the authors' earlier paper [Ann. Pure Appl. Logic 33, 213-243 (1987; Zbl 0634.03047)]. The proof is obtained from the previous one by deleting all references to the notion of ``depth'', and the model is built by iteration of Miller's rational perfect set forcing.