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, which is an R-branching tree with no infinite branches. The existence of such a hierarchy sheds some light on the hidden complexity of $(R^ω,>_\lex)$.
A hierarchy of chains embeddable into the lexicographic power $R^\omega_\lex$
GIARLOTTA, Alfio;
2013-01-01
Abstract
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, which is an R-branching tree with no infinite branches. The existence of such a hierarchy sheds some light on the hidden complexity of $(R^ω,>_\lex)$.File in questo prodotto:
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