Indivisible Sequences and Descendability

Abstract

We introduce the notion of indivisible sequences and show that to any indivisible sequence $\{S,\hat{I}¨:S\to R\}$ we can associate faithfully flat ring maps $R\to R^{\prime }$ that are not descendable. As a corollary, we obtain the first example of a faithfully flat ring map between ${\aleph }_{n-1}$-countable rings that has descendability exponent $n$, and indeed a faithfully flat ring map between ${\aleph }_{\ddot{I}}‰$-countable rings that is not descendable.