| This resource is not discoverable in the library. If the resource was recently submitted, it may require some time before it becomes discoverable through this search service. | | Resource Title: | a shorter proof: Martin's axiom and the continuum hypothesis
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| Description: | This is another, shorter, proof for the fact that ... always holds. Let ... be a partially ordered set and ... be a collection of subsets of P. We remember that a filter G on ... is ... -generic if ... for all ... which are dense in ... . (In this context ... means: If D is dense in ... , then for every ... there's a ... such that ... .) Let ... be a partially ordered set and ... a countable collection of dense subsets of P. Then there exists a ... -generic filter G on P. Moreover, it could be shown that for every ... there's such a ... -generic filter G with ... . ... Let ... be the dense subsets in ... . Furthermore let ... . Now we can choose for every ... an element ... such that ... and ... . If we now consider the set ... , then it is easy to check that G is a ... -generic filter on P and ... obviously. This completes the proof. ... |
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