On the consistency and independence of some set-theoretical axioms

@article{Abian1978OnTC,
title={On the consistency and independence of some set-theoretical axioms},
author={A. Abian and S. Lamacchia},
journal={Notre Dame J. Formal Log.},
year={1978},
volume={19},
pages={155-158}
}

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… Expand