CCC posets of perfect trees
Chain conditions in maximal models
We present two varations which create maximal models relative to certain counterexamples to Martin’s Axiom, in hope of separating certain classical statements which fall between MA and Suslin’s Hypothesis. One of these models is taken from [19], in which we maximize relative to the existence of a certain type of Suslin tree, and then force with that tree. In the resulting model, all Aronszajn trees are special and Knaster’s forcing axiom ₃ fails. Of particular interest is the still open question...
Characterizations of certain classes of posets having Gs-lattices of a relatively small size
Cohen real and disjoint refinement of perfect sets
We prove that if there exists a Cohen real over a model, then the family of perfect sets coded in the model has a disjoint refinement by perfect sets.
Coherent adequate sets and forcing square
We introduce the idea of a coherent adequate set of models, which can be used as side conditions in forcing. As an application we define a forcing poset which adds a square sequence on ω₂ using finite conditions.
Collapsing algebras and Suslin trees
Collapsing of cardinals in generalized Cohen's forcing
Connections between different amoeba algebras
Continuous relations and generalized sets
Correction to: Adding a random or a Cohen real: topological consequences and the effect on Martin's axiom