Abstract:The paper contains a~self-contained alternative proof of my Theorem in \textit{Characterization of generic extensions of models of set theory\/}, Fund. Math. {\bf 83} (1973), 35--46, saying that for models $M\subseteq N$ of {\bf ZFC} with same ordinals, the condition $Apr_{M,N}(\kappa)$ implies that $N$ is a~$\kappa$-C.C. generic extension of $M$.
Keywords: inner model; extension of an~inner model; $\kappa$-generic extension; $\kappa$-C.C. generic extension; $\kappa$-boundedness condition; $\kappa$ approximation condition; Boolean ultrapower; Boolean valued model
DOI: DOI 10.14712/1213-7243.2015.209
AMS Subject Classification: 03E45 03E40