We introduce an apparent strengthening of Sufficient Cohesion that we call Stable Connected Codiscreteness (SCC) and show that if $p: E --> S$ is cohesive and satisfies SCC then the internal axiom of choice holds in $S$. Moreover, in this case, $p^!: S --> E$ is equivalent to the inclusion $E_{\neg\neg} --> E$.
Keywords: Axiomatic cohesion, Topos theory
2010 MSC: 18B25, 03G30, 18F99
Theory and Applications of Categories, Vol. 30, 2015, No. 26, pp 909-932.
Published 2015-06-30.
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