Postgraduate workshop on Alternative Set Theories

Amsterdam, The Netherlands

22 to 24 June 2013


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 non-trivial 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 well-behaved 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.