The relation between the height of a well-founded partial ordering and the order types of its chains and antichains
暂无分享,去创建一个
We show that a well-founded partial ordering of countable height α must contain either a chain of order type α or an antichain of order type ω. On the other hand, there are partial orderings of arbitrary countable height with no infinite chains and no antichains of order type (ω+1).
[1] E. C. Milner,et al. On Chains and Antichains in well Founded Partially Ordered Sets , 1981 .
[2] Frank Plumpton Ramsey,et al. On a Problem of Formal Logic , 1930 .
[3] Ernst Specker,et al. Teilmengen von Mengen mit Relationen , 1956 .
[4] E. S. Wolk. Partially well ordered sets and partial ordinals , 1967 .