[FOM] Reflective well-founded relations

martdowd at aol.com martdowd at aol.com
Wed Mar 30 19:24:55 EDT 2016

"Reflective well-founded relations" has just been submitted, and is
temporarily available at my web site.

If $\kappa$ is an inaccessible cardinal and $\phi$ defines a WF
(well-founded relation) $R$ in $V_\kappa$, say that $\phi$ relects
at $\lambda$ if it defines a WF at $\lambda$.  Say that $R$ is reflective
if there is a stationary set of $\lambda$ at which $\phi$ reflects.

By generalizing the results of "Sigma-1-1 Well-Founded Relations and Set
Chains", new axioms for set theory are given which make use of such WF's.

It is also shown that as $S$ gets smaller the heights of the WFs' increase,
whence if $V=L$ the chain lengths do.

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