Semimorasses and nonreflection at singular cardinals Original Research Article

Some subfamilies of View the MathML sourceκ(λ), for κ regular, κ ⩽ λ, called (κ, λ)-semimorasses are investigated. For λ = κ+, they constitute weak versions of Vellemanʹs simplified (κ, 1)-morasses, and for λ > κ+, they provide a combinatorial framework which in some cases has similar applications to the application of (κ, 1)-morasses with this difference that the obtained objects are of size λ ⩾ κ+, and not only of size κ+ as in the case of morasses. New consistency results involve (compatible with CH) existence of nonreflecting objects of singular sizes of uncountable cofinality such as a nonreflecting stationary set in View the MathML sourceκ(λ), a nonreflecting nonmetrizable space of size λ, a nonreflecting nonspecial tree of size λ. We also characterize possible minimal sizes of nonspecial trees without uncountable branches.