We continue the investigation of Gregory trees and the Cantor Tree Property carried out by Hart and Kunen. We produce models of MA with the Continuum arbitrarily large in which there are Gregory trees, and in which there are no Gregory trees.
"Gregory trees, the continuum, and Martin's axiom." J. Symbolic Logic 74 (2) 712 - 720, June 2009. https://doi.org/10.2178/jsl/1243948337