The smallest common extension of a sequence of models of ZFC

Lev Bukovský; Jaroslav Skřivánek

Commentationes Mathematicae Universitatis Carolinae (1994)

  • Volume: 35, Issue: 4, page 745-752
  • ISSN: 0010-2628

Abstract

top
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 is sometimes the smallest common extension of this sequence and very often it is not.

How to cite

top

Bukovský, Lev, and Skřivánek, Jaroslav. "The smallest common extension of a sequence of models of ZFC." Commentationes Mathematicae Universitatis Carolinae 35.4 (1994): 745-752. <http://eudml.org/doc/247633>.

@article{Bukovský1994,
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.},
author = {Bukovský, Lev, Skřivánek, Jaroslav},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {model of ZFC; generic extension; rigid Boolean algebra; hereditary $M$-definable; generic extension; iterated forcing; rigid Boolean algebra; finite support iteration; Cohen real},
language = {eng},
number = {4},
pages = {745-752},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The smallest common extension of a sequence of models of ZFC},
url = {http://eudml.org/doc/247633},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Bukovský, Lev
AU - Skřivánek, Jaroslav
TI - The smallest common extension of a sequence of models of ZFC
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 4
SP - 745
EP - 752
AB - 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.
LA - eng
KW - model of ZFC; generic extension; rigid Boolean algebra; hereditary $M$-definable; generic extension; iterated forcing; rigid Boolean algebra; finite support iteration; Cohen real
UR - http://eudml.org/doc/247633
ER -

References

top
  1. Blass A., The model of set generated by countable many generic reals, J. Symbolic Logic 46 (1981), 732-752. (1981) MR0641487
  2. Bukovský L., Characterization of generic extensions of models of set theory, Fund. Math. 83 (1973), 35-46. (1973) MR0332477
  3. Bukovský L., A general setting of models extensions, International Workshop on Set theory, Abstracts of the talks, Marseilles-Luminy (1990). (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. (1989) Zbl0673.03042MR0994389
  5. Jech T., Set Theory, Academic Press New York (1978). (1978) Zbl0419.03028MR0506523
  6. Solovay R., Tennenbaum S., Iterated Cohen Extensions and Souslin`s Problem, Ann. of Math. 94 (1971), 201-245. (1971) Zbl0244.02023MR0294139
  7. Štěpánek P., Embeddings and automorphisms, Handbook of Boolean algebras J.D. Monk and R. Bonnet North-Holland Amsterdam (1989), 607-635. (1989) MR0991604
  8. Vopěnka P., Hájek P., The Theory of Semisets, Academia Prague (1972). (1972) MR0444473

NotesEmbed ?

top

You must be logged in to post comments.