For strong arithmetizable theories T there exists a primitive recursive selector that proves every instance of the consistency schema, yielding uniformity that cannot be internalized as the single sentence Con(T).
Steiner, Review of Michael Detlefsen, Hilbert's Program: An Essay on Mathematical Instrumentalism, Journal of Philosophy 88 (1991), no
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Uniformity of Consistency in Arithmetic and G\"odel's Second Incompleteness Theorem: Ein M\"archen
For strong arithmetizable theories T there exists a primitive recursive selector that proves every instance of the consistency schema, yielding uniformity that cannot be internalized as the single sentence Con(T).