On automorphisms of Boolean algebras embedded in P (ω)/fin

Magdalena Grzech

Fundamenta Mathematicae (1996)

  • Volume: 150, Issue: 2, page 127-147
  • ISSN: 0016-2736

Abstract

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We prove that, under CH, for each Boolean algebra A of cardinality at most the continuum there is an embedding of A into P(ω)/fin such that each automorphism of A can be extended to an automorphism of P(ω)/fin. We also describe a model of ZFC + MA(σ-linked) in which the continuum is arbitrarily large and the above assertion holds true.

How to cite

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Grzech, Magdalena. "On automorphisms of Boolean algebras embedded in P (ω)/fin." Fundamenta Mathematicae 150.2 (1996): 127-147. <http://eudml.org/doc/212166>.

@article{Grzech1996,
abstract = {We prove that, under CH, for each Boolean algebra A of cardinality at most the continuum there is an embedding of A into P(ω)/fin such that each automorphism of A can be extended to an automorphism of P(ω)/fin. We also describe a model of ZFC + MA(σ-linked) in which the continuum is arbitrarily large and the above assertion holds true.},
author = {Grzech, Magdalena},
journal = {Fundamenta Mathematicae},
keywords = {embedding into ; continuum hypothesis; Martin's axiom; Boolean algebra; automorphism},
language = {eng},
number = {2},
pages = {127-147},
title = {On automorphisms of Boolean algebras embedded in P (ω)/fin},
url = {http://eudml.org/doc/212166},
volume = {150},
year = {1996},
}

TY - JOUR
AU - Grzech, Magdalena
TI - On automorphisms of Boolean algebras embedded in P (ω)/fin
JO - Fundamenta Mathematicae
PY - 1996
VL - 150
IS - 2
SP - 127
EP - 147
AB - We prove that, under CH, for each Boolean algebra A of cardinality at most the continuum there is an embedding of A into P(ω)/fin such that each automorphism of A can be extended to an automorphism of P(ω)/fin. We also describe a model of ZFC + MA(σ-linked) in which the continuum is arbitrarily large and the above assertion holds true.
LA - eng
KW - embedding into ; continuum hypothesis; Martin's axiom; Boolean algebra; automorphism
UR - http://eudml.org/doc/212166
ER -

References

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  1. [1] J. Baumgartner, R. Frankiewicz and P. Zbierski, Embeddings of Boolean algebras in P(ω)/fin, Fund. Math. 136 (1990), 187-192. Zbl0718.03039
  2. [2] R. Frankiewicz, Some remarks on embeddings of Boolean algebras and topological spaces II, Fund. Math. 126 (1985), 63-67. Zbl0579.03037
  3. [3] R. Frankiewicz and P. Zbierski, Partitioner-representable algebras, Proc. Amer. Math. Soc. 103 (1988), 926-928. Zbl0655.03036
  4. [4] R. Frankiewicz and P. Zbierski, On a theorem of Baumgartner and Weese, Fund. Math. 139 (1991), 167-175. Zbl0766.03028
  5. [5] R. Frankiewicz and P. Zbierski, Hausdorff Gaps and Limits, North-Holland, 1994. Zbl0821.54001
  6. [6] K. Kunen, Set Theory. An Introduction to Independence Proofs, North-Holland, 1980. 
  7. [7] R. Sikorski, Boolean Algebras, Springer, Berlin, 1969. 

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