Monads in basic equivalences. (English) Zbl 0531.03032

Čuda, K.; Kussová, B.

Commentat. Math. Univ. Carol. 24, 437-452 (1983).

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

Keywords:

alternative set theory; basic equivalence; monad; definability; similarity; endomorphism