Abstracts.
Zachiri McKenzie (Cambridge),
Automorphisms of models of set theory and
extensions of "New Foundations" with Urelements
The talk will begin with a brief introduction to the set theory NFU that was first
proposed by Ronald Jensen in 1969. This theory is obtained by weakening the axiom of
Extensionality Quine's "New Foundations" set theory to allow urelements into the domain of
discourse. Jensen showed that models of NFU can be obtained from models of subsystems of
ZFC that admit nontrivial automorphism. I will mention some natural extensions of NFU and
indicate how models of these theories can be obtained from models of set theories that
admit certain wellbehaved automorphisms. I will then discuss some recent results which
separate the consistency strengths of two relatively weak extensions of NFU. I will
conclude by mentioning some open questions.
