[FOM] New paper on function chains

[martdowd at aol.com]

I have just submitted "Downsets and Generalized Descriptive Set Theory" to
IJPAM, and made it temporarily available at my web site.  In it the
following are proved:
 - An inaccessible cardinal $\kappa$ is weakly compact iff, whenever $T$ is
 a tree with no length $\kappa$ branches, there is an inaccessible
 cardinal $\lambda<\kappa$ such that $T\cap V_{\lambda}$ has no branch
 of length $\lambda$.
 - If $V=L$, and there is a $Sigma^1_1$ WPS of order type $\alpha$, then
 there is a WPS uniformly defined in inaccessibles, of order type $\alpha$.
 (As a result, there are function chains of length $\alpha$).

- Martin Dowd

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