Archive for Mathematical Logic

, Volume 58, Issue 1–2, pp 137–153 | Cite as

An extension of Shelah’s trichotomy theorem

  • Shehzad AhmedEmail author


Shelah (Algorithms Comb 14:420–459, 1997) develops the theory of \(\mathrm {pcf}_I(A)\) without the assumption that \(|A|<\min (A)\), going so far as to get generators for every \(\lambda \in \mathrm {pcf}_I(A)\) under some assumptions on I. Our main theorem is that we can also generalize Shelah’s trichotomy theorem to the same setting. Using this, we present a different proof of the existence of generators for \(\mathrm {pcf}_I(A)\) which is more in line with the modern exposition. Finally, we discuss some obstacles to further generalizing the classical theory.


pcf theory Trichotomy Generators 

Mathematics Subject Classification



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, 321 Morton HallOhio UniversityAthensUSA

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