The urelements in the usual models of NFU are discernible
by
M. Randall Holmes
Boise State University

The usual construction of models of NFU (Jensen's modification of Quine's set theory New Foundations

which allows urelements) will be described. A natural question arises as to whether the urelements of these

models are indiscernible. There are superficial reasons to believe that they are. This turns out not to be the case

for a somewhat surprising reason: when a model of NFU is constructed in the usual way, all information

about the extension of the model elements to be interpreted as urelements may appear to have been discarded,

but in fact the membership relation of the original model of set theory from which the model of NFU

was constructed turns out to be first-order definable in terms of the membership relation of the model of NFU,

from which it follows that the urelements of the model of NFU are easily distinguished from one another using information about

their extensions in the original model. This result was surprising to the author.

Date received: March 22, 2007