Geodesic
The smallest common extension of a sequence of models of ZFC
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 4, pp. 745-752

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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.
Classification : 03C62, 03E40, 03E45
Keywords: model of ZFC; generic extension; rigid Boolean algebra; hereditary $M$-definable 
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     title = {The smallest common extension of a sequence of models of {ZFC}},
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Bukovský, Lev; Skřivánek, Jaroslav. The smallest common extension of a sequence of models of ZFC. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 4, pp. 745-752. http://geodesic.mathdoc.fr/item/CMUC_1994__35_4_a15/