The wholeness axiom and Laver sequences

@article{Corazza2000TheWA,
  title={The wholeness axiom and Laver sequences},
  author={Paul Corazza},
  journal={Ann. Pure Appl. Logic},
  year={2000},
  volume={105},
  pages={157-260}
}
In this paper we introduce the Wholeness Axiom (WA), which asserts that there is a nontrivial elementary embedding from V to itself. We formalize the axiom in the language {∈; j}, adding to the usual axioms of ZFC all instances of Separation, but no instance of Replacement, for j-formulas, as well as axioms that ensure that j is a nontrivial elementary embedding from the universe to itself. We show that WA has consistency strength strictly between I3 and the existence of a cardinal that is… CONTINUE READING

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