Explaining maximality through the hyperuniverse programme
pp. 185-204
in: Carolin Antos, Radek Honzik, Claudio Ternullo, Sy D. Friedman (eds), The hyperuniverse project and maximality, Berlin, Springer, 2018Abstract
The (maximal) iterative concept of set is standardly taken to justify ZFC and some of its extensions. In this paper, we show that the maximal iterative concept also lies behind a class of further maximality principles expressing the maximality of the universe of sets V in height and width. These principles have been heavily investigated by the first author and his collaborators within the Hyperuniverse Programme. The programme is based on two essential tools: the hyperuniverse, consisting of all countable transitive models of ZFC, and V -logic, both of which are also fully discussed in the paper.