In mathematics, a (κ,n)-morass is a specific structure M of "height" κ and "gap" n for any uncountable regular cardinal κ and natural number n ≥ 1.
The original definition and applications of gap-1 and higher gap (ordinary) morasses, invented by Ronald Jensen, are complicated ones, see eg.
Velleman defined much simpler structures for n = 1 and showed that the existence of gap-1 morasses is equivalent to the existence of gap-1 simplified morasses.
Roughly speaking: a (κ,1)-simplified morass M = < φ→, F⇒ > contains a sequence φ→ = < φβ : β ≤ κ > of ordinals such that φβ < κ for β < κ and φκ = κ+, and a double sequence F⇒ = < Fα,β : α < β ≤ κ > where Fα,β are collections of monotone mappings from φα to φβ for α<β ≤ κ with specific (easy but important) conditions.
Velleman's clear definition can be found in, where he also constructed (ω0,1) simplified morasses in ZFC. In he gave similar simple definitions for gap-2 simplified morasses, and in he constructed (ω0,2) simplified morasses in ZFC.
Higher gap simplified morasses for any n ≥ 1 were defined by Morgan and Szalkai,.
Roughly speaking: a (κ,n + 1)-simplified morass (of Szalkai) M = < M→, F⇒ > contains a sequence M→ = < Mβ : β ≤ κ > of (< κ,n)-simplified morass-like structures for β < κ , Mκ is a (κ+,n) -simplified morass, and a double sequence F⇒ = < Fα,β : α < β ≤ κ > where Fα,β are collections of mappings from Mα to Mβ for α < β ≤ κ with specific conditions.
Quagmires are similar, morass-like structures in set theory.