2013/04/02 by Tarek Sayed Ahmed, Ahmed, Tarek Sayed · 1 citation
Mathematics · #FOS: Mathematics #Logic (math.LO) #math.LO
paper · pdf · doi:10.48550/arxiv.1304.0761
arXiv admin note: substantial text overlap with arXiv:1303.7386, arXiv:1304.0712; and overlap with arXiv:math/0508572 by other author without attribution
arxiv created 2013/04/02 · arxiv updated 2013/04/04
We show that quasi-projective relation algebras and directed cylindric algebras are equivalent categorialy. We work out a Godels second incompleteness theorem for finite varibale fragments of first order logic. We show that distinct set theories (like one with CH, and another with its negation) give rise to equationally distinct simple directed cylindric algebras. This correspondance was worked out for quasi projective relation algebras (with a distinguished element corresponding to membership relation). The idea of the proof is that the Sagi representation of directed cylindric algebras preserve well-foundnes. Finally, using that the functor defined preserves order, we show that the class of directed cylindric algebras have the superamalgmation property.