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Keywords:
model of ZFC; generic extension; rigid Boolean algebra; hereditary $M$-definable
model of ZFC; generic extension; rigid Boolean algebra; hereditary $M$-definable
Summary:
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.
References:
[1] Blass A.: The model of set generated by countable many generic reals. J. Symbolic Logic 46 (1981), 732-752. MR 0641487
[2] Bukovský L.: Characterization of generic extensions of models of set theory. Fund. Math. 83 (1973), 35-46. MR 0332477
[3] Bukovský L.: A general setting of models extensions. International Workshop on Set theory, Abstracts of the talks, Marseilles-Luminy (1990).
[4] Ciesielski K., Guzicki W.: Generic families and models of set theory with the axiom of choice. Proc. Amer. Math. Soc. 106 (1989), 199-206. MR 0994389 | Zbl 0673.03042
[5] Jech T.: Set Theory. Academic Press New York (1978). MR 0506523 | Zbl 0419.03028
[6] Solovay R., Tennenbaum S.: Iterated Cohen Extensions and Souslin`s Problem. Ann. of Math. 94 (1971), 201-245. MR 0294139 | Zbl 0244.02023
[7] Štěpánek P.: Embeddings and automorphisms. Handbook of Boolean algebras J.D. Monk and R. Bonnet North-Holland Amsterdam (1989), 607-635. MR 0991604
[8] Vopěnka P., Hájek P.: The Theory of Semisets. Academia Prague (1972). MR 0444473
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