On the consistency and independence of some set-theoretical axioms

  title={On the consistency and independence of some set-theoretical axioms},
  author={Alexander Abian and Samuel Lamacchia},
  journal={Notre Dame J. Formal Log.},
In this paper by means of simple models it is shown that the five set-theoretical axioms of Extensionalit y, Replacement, Power-Set, SumSet, and Choice are consistent and that each of the axioms of Extensionality, Replacement, and Power-Set is independent from the remaining four axioms. Although the above results are known and can be found in part in [l], it is believed that this paper has some expository merits. The abovementioned axioms are five of the six axioms of the ZermeloFraenkel Theory… 
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