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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Pairwise incompatible generic families


Author: Wojciech Guzicki
Journal: Proc. Amer. Math. Soc. 110 (1990), 1049-1053
MSC: Primary 03C62; Secondary 03E25
DOI: https://doi.org/10.1090/S0002-9939-1990-1019750-5
MathSciNet review: 1019750
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Abstract: Let $ M$ be a countable model of $ {\mathbf{Z}}{{\mathbf{F}}^ - }$. There exists a family $ \mathcal{F}$ of $ {2^{{2^\omega }}}$ models of $ {\mathbf{Z}}{{\mathbf{F}}^ - }$ each obtained from $ M$ by adjoining an $ M$-generic family of $ {2^\omega }$ Cohen reals, such that no two distinct models in $ \mathcal{F}$ have a common extension to a model of $ {\mathbf{Z}}{{\mathbf{F}}^ - }$ with the same ordinals.


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DOI: https://doi.org/10.1090/S0002-9939-1990-1019750-5
Article copyright: © Copyright 1990 American Mathematical Society

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