A Hierarchy of Chains Embeddable into the Lexicographic Power (R ω , ≺lex)
Alfio Giarlotta · 2013
A hierarchy of chains is a transfinite sequence of linear orderings such that each chain in the sequence order-embeds into all chains following it but not in those preceding it. We construct a c + -long hierarchy of chains that order-embed into the lexicographic power (R ω , ≺lex). Each linear ordering L in this hierarchy is such that there exists a tree representation of L ,w hich is anR-branching tree with no infinite branches. The existence of such a hierarchy sheds some light on the hidden