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Monads in basic equivalences. (English) Zbl 0531.03032

Summary: In this paper we prove that all sets from the universe of sets can be defined from both any arbitrary proper \(Sd_ V\) class and a suitable monad in any equivalence of indiscernibility. We also show that there is a monad \(\mu\) such that \(Def_{\mu}\neq V\). These facts are further used for proving some interesting assertions concerning similarities; e.g. it is shown here that some special cases of similarities have to be parts of identity.

MSC:

03E70 Nonclassical and second-order set theories
54J05 Nonstandard topology
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