May 8
James Cummings,
Carnegie Mellon University
Compactness and minimality properties for linear orderings
Let $\Phi$ be a property of linear orderings such that if $L$ has $\Phi$ and $L$ is bi-embeddable with $L'$ then $L'$ has $\Phi$.
We discuss some situations where:
A) (Incompactness) $L$ does not have $ hi$ but every strictly smaller suborder of $L$ has $\Phi$.
B) (Minimality) $L$ does not have $\Phi$, and $L$ embeds into every subordering of $L$ which does not have $\Phi$.