Take the 2-minute tour ×  Hi all! Is there anything like Gödel's
constructible universe for New Foundations?  More precisely, I
would like a process for taking a model $M$ of NF, and using it
to build a model $L \subseteq M$ of NF with the property that
every set in $L$ is defined by a (stratified) first-order
formula with quantifiers ranging over $M$. (Edited; see the
comments for a discussion of some issues surrounding this
definition.)  Anything not exactly that, but along those lines,
would also be of interest. I would also be interested in hearing
about such results for non-well-founded set theories other than
NF. Has this been done? Is it possible?  I'm wondering because I
am trying to build this sort of constructible model for a naïve
set theory that I am studying. I haven't figured out how to
apply the methods used for models of ZF to models of naïve set
theory. I'm guessing that similar issues might apply in working
with NF, because both theories are primarily distinguished by
their use of a powerful