I am beginning a study in set theory and I found an old book in my school's library by Martin Zuckeman called Sets and Transfinite Numbers which was published in the 1970's. Has anyone used this text ...
$F$ is Dedekind-finite if for every $A\varsubsetneq F$ we have $A<_cF$. Need help to prove that if $F,G$ are Dedekind-finite sets, $F\cap G=\emptyset$ then $F\cup G$ is also Dedekind-finite. ...
Working under Zermelo-Franenkel set theory. how I can prove following: Let $V$ be proper class. Let $F : V \rightarrow U$ be a one-one function. Then $U$ has to be a proper class.