The Wholeness Axioms and the Class of Supercompact Cardinals
We show that certain relatively consistent structural properties of the class of supercompact cardinals are also relatively consistent with the Wholeness Axioms.
Trees, inverse systems, and valuated vector spaces
Uniqueness of means in the Cohen model
We investigate the question of whether or not an amenable subgroup of the permutation group on can have a unique invariant mean on its action. We extend the work of M. Foreman (1994) and show that in the Cohen model such an amenable group with a unique invariant mean must fail to have slow growth rate and a certain weakened solvability condition.
Universality and strong extensionality.
Weak foundation and axioms of universality.
Weak square sequences and special Aronszajn trees
A classical theorem of set theory is the equivalence of the weak square principle with the existence of a special Aronszajn tree on μ⁺. We introduce the notion of a weak square sequence on any regular uncountable cardinal, and prove that the equivalence between weak square sequences and special Aronszajn trees holds in general.
О возможном решении обобщенной континиум-проблемы.