An ordering (≤K) on maximal almost disjoint (MAD) families closely related to destructibility of MAD families by forcing is introduced and studied. It is shown that the order has antichains of size 𝔠 and decreasing chains of length 𝔠+ bellow every element. Assuming 𝔱 =𝔠 a MAD family equivalent to all of its restrictions is constructed. It is also shown here that the Continuum Hypothesis implies that for every ω&ω-bounding forcing ℙ of size 𝔠 there is a Cohen-destructible, ℙ-indestructible MAD family. Finally, two other orderings on MAD families are suggested and an old construction of Mrówka is revisited.
"Ordering MAD families a la Katětov." J. Symbolic Logic 68 (4) 1337 - 1353, December 2003. https://doi.org/10.2178/jsl/1067620190