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arXiv · 1706.09018

An Extension of Shelah's Trichotomy Theorem

Shehzad Ahmed
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Abstract

In Sh506, Shelah 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.

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BibTeXRIS

Shehzad Ahmed. 2017-06-27. An Extension of Shelah's Trichotomy Theorem. https://doi.org/10.1007/s00153-018-0631-6

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