# Article

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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
Summary:
The paper contains a self-contained alternative proof of my Theorem in Characterization of generic extensions of models of set theory, Fund. Math. 83 (1973), 35--46, saying that for models $M\subseteq N$ of ZFC with same ordinals, the condition $Apr_{M,N}(\kappa)$ implies that $N$ is a $\kappa$-C.C. generic extension of $M$.
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