Abstract:
<jats:title>Abstract</jats:title><jats:p>1. If <jats:italic>A</jats:italic> is strongly amorphous (i.e., all relations on <jats:italic>A</jats:italic> are definable), then its power set <jats:italic>P(A)</jats:italic> is dually Dedekind infinite, i. e., every function from <jats:italic>P(A)</jats:italic> onto <jats:italic>P(A)</jats:italic> is injective. 2. The class of “inexhaustible” sets is not closed under supersets unless AC holds.</jats:p>
Description:
<jats:title>Abstract</jats:title><jats:p>1. If <jats:italic>A</jats:italic> is strongly amorphous (i.e., all relations on <jats:italic>A</jats:italic> are definable), then its power set <jats:italic>P(A)</jats:italic> is dually Dedekind infinite, i. e., every function from <jats:italic>P(A)</jats:italic> onto <jats:italic>P(A)</jats:italic> is injective. 2. The class of “inexhaustible” sets is not closed under supersets unless AC holds.</jats:p>