2017/09/20 by Tomáš Lávička, Lávička, Tomáš, Jonathan L. Verner +1
Computer Science · Decision Sciences · Medicine · #Auction Theory and Applications #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #Logic, Reasoning, and Knowledge #Platelet Disorders and Treatments
paper · pdf · doi:10.48550/arxiv.1709.06862
openalex publication_date 2017/09/20 · openalex created_date 2022/09/03 · openalex updated_date 2026/07/28
We show in ZFC that the existence of completely separable maximal almost disjoint families of subsets of ω implies that the modal logic S4.1.2 is complete with respect to the Čech-Stone compactification of the natural numbers, the space βω. In the same fashion we prove that the modal logic S4 is complete with respect to the space ω^*=βω∖ω. This improves the results of G. Bezhanishvili and J. Harding who prove these theorems under stronger assumptions (\mathfraka=\mathfrakc). Our proof is also somewhat simpler.