Corpus ID: 119150551

Amalgamating many overlapping Boolean algebras

@article{Milovich2016AmalgamatingMO,
  title={Amalgamating many overlapping Boolean algebras},
  author={D. Milovich},
  journal={arXiv: Logic},
  year={2016}
}

D. Milovich

Published 2016

Mathematics

arXiv: Logic

In general, two overlapping Boolean algebras always extend to a common Boolean algebra, but three may not. We prove a new sufficient condition for $n$ overlapping Boolean algebras to have a common extension. Combining this with the set-theoretic technique of long $\omega_1$-approximation sequences (also known as Davies sequences), we obtain a flexible method of constructing (in ZFC) arbitrarily large Boolean algebras as direct limits of countable Boolean algebras. Along the way, we develop some… CONTINUE READING

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