Chains and antichains in Boolean algebras

M. Losada; Stevo Todorčević

Fundamenta Mathematicae (2000)

  • Volume: 163, Issue: 1, page 55-76
  • ISSN: 0016-2736

Abstract

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We give an affirmative answer to problem DJ from Fremlin’s list [8] which asks whether M A ω 1 implies that every uncountable Boolean algebra has an uncountable set of pairwise incomparable elements.

How to cite

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Losada, M., and Todorčević, Stevo. "Chains and antichains in Boolean algebras." Fundamenta Mathematicae 163.1 (2000): 55-76. <http://eudml.org/doc/212429>.

@article{Losada2000,
abstract = {We give an affirmative answer to problem DJ from Fremlin’s list [8] which asks whether $MA_\{ω_1\}$ implies that every uncountable Boolean algebra has an uncountable set of pairwise incomparable elements.},
author = {Losada, M., Todorčević, Stevo},
journal = {Fundamenta Mathematicae},
keywords = {chains; antichains; Boolean algebras},
language = {eng},
number = {1},
pages = {55-76},
title = {Chains and antichains in Boolean algebras},
url = {http://eudml.org/doc/212429},
volume = {163},
year = {2000},
}

TY - JOUR
AU - Losada, M.
AU - Todorčević, Stevo
TI - Chains and antichains in Boolean algebras
JO - Fundamenta Mathematicae
PY - 2000
VL - 163
IS - 1
SP - 55
EP - 76
AB - We give an affirmative answer to problem DJ from Fremlin’s list [8] which asks whether $MA_{ω_1}$ implies that every uncountable Boolean algebra has an uncountable set of pairwise incomparable elements.
LA - eng
KW - chains; antichains; Boolean algebras
UR - http://eudml.org/doc/212429
ER -

References

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  14. [14] W. Sierpiński, Sur un problème de la théorie des relations, Ann. Scuola Norm. Sup. Pisa (2) 2 (1933), 285-287. Zbl0007.09702
  15. [15] S. Todorčević, Trees and linearly ordered sets, in: Handbook of Set-Theoretic Topology, Elsevier, Amsterdam, 1984, 235-293. 
  16. [16] S. Todorčević, Remarks on chain conditions in products, Compositio Math. 55 (1985), 295-302. Zbl0583.54003
  17. [17] S. Todorčević, Remarks on cellularity in products, ibid. 57 (1986), 357-372. Zbl0616.54002
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  19. [19] S. Todorčević, Irredundant sets in Boolean algebras, Trans. Amer. Math. Soc. 339 (1993), 35-44. Zbl0781.06010

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