Isomorphism and higher order equivalence

✍ Scribed by M. Ajtai

• Publisher: Elsevier Science
• Year: 1979
• Weight: 833 KB
• Volume: 16
• Category: Article
• ISSN: 0003-4843
• DOI: 10.1016/0003-4843(79)90001-9

✦ Synopsis

A (K, A) tree is normal if

Vx ~ T3y, z ~ T(y fi z A y < x A z < x A h,r(y) = h,r(Z) --hT(x)+ 1),

The elements p, q of an arbitrary partially ordered set P are called incompatible if they have no common lower bound in P. An antichain is a set of pairwise incompatible elements in P.

B is an a-branch of the tree T if it is a linearly ordered subset of T and

Vfl < a ::l!x ~ Bh-r(X) = ft.

A Suslin tree is a normal (~ol, to~) tree, with no uncountable antichain. Let T be a tree

T~={y~T[y~x} if x~T.