Two examples of Borel partially ordered sets with the countable chain condition
Author:
Stevo Todorčević
Journal:
Proc. Amer. Math. Soc. 112 (1991), 1125-1128
MSC:
Primary 03E05; Secondary 03E15, 54H05
DOI:
https://doi.org/10.1090/S0002-9939-1991-1069693-7
MathSciNet review:
1069693
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Abstract: We define an open symmetric two-place relation on the reals such that the reals cannot be covered by countably many sets of related elements, but there is no uncountable set of unrelated elements. The poset of finite sets of related elements satisfies the countable chain condition but it may fail to have the property K, i.e., a substantial irregularity can be injected in
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1991-1069693-7
Article copyright:
© Copyright 1991
American Mathematical Society