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Nonvanishing derived limits without scales
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DOI：10.1007/s00153-025-00996-z.png)
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Abstract
En 中文
The derived functors lim(n) of the inverse limit are widely studied for their topological applications, among which are some repercussions on the additivity of strong homology. Set theory has proven useful in dealing with these functors, for instance in the case of the inverse system A of abelian groups indexed over (omega)omega. So far, consistency results for nonvanishing derived limits of A have always assumed the existence of a scale (i.e. a linear cofinal subset of ((omega)omega, <=*), or equivalently that b=d). Here we eliminate that assumption and prove that nonvanishing derived limits, and hence the non-additivity of strong homology, are consistent with any value of aleph 1 <= b <= d < aleph(omega), thus giving a partial answer to a question of Bannister.
Keywords:
Derived limits
Strong homology
Cardinal characteristics
Weak diamond
Journal
A
IF:
0.4
Papers:
34
Citations:
0