## Lev Bukovsk\'y, Jaroslav Sk\v riv\'anek

*The smallest common extension of a sequence of models of ZFC *

Comment.Math.Univ.Carolinae 35,4 (1994) 745-752. **Abstract:**In this note, we show that the model obtained by finite support iteration of a sequence of generic extensions of models of ZFC of length $\omega $ is sometimes the smallest common extension of this sequence and very often it is not.

**Keywords:** model of ZFC, generic extension, rigid Boolean algebra, hereditary $M$-definable

**AMS Subject Classification:** Primary 03E40; Secondary 03E45

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