Countable chain condition in partition calculus
نویسندگان
چکیده
منابع مشابه
Compact spaces, elementary submodels, and the countable chain condition
Given a space 〈X,J 〉 in an elementary submodel M of H(θ), define XM to be X ∩ M with the topology generated by {U ∩ M : U ∈ J ∩ M}. It is established, using anti-large-cardinals assumptions, that if XM is compact and its regular open algebra is isomorphic to that of a continuous image of some power of the two-point discrete space, then X = XM . Assuming CH+SCH (the Singular Cardinals Hypothesis...
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The assumption of [HM] and our assumption here, the existence of a strong partition cardinal, is moderately special. On the one hand, it violates the Axiom of Choice and is not relatively consistent with ZF (unlike AC and its negation). On the other hand, under the Axiom of Determinacy (AD), such cardinals are abundant and consistent with countable choice and DC, the principle of Dependent Choi...
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In order to make (19) correct we define X., S(n) (n<(o) a little more caref lly and replace lines 21-31 on Page 504 by the following : Let n < co and s ppose that we have already chosen elements xi c S (ia+a, then choose sets A,A'cA(' ) s ch that A<A' ; if on the other hand a~a+a, then ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1998
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(97)00256-2