Por Anton Freund (Technische Universität Darmstadt).

Timothy Carlson's patterns of resemblance offer an astonishingly simple way to describe large computable ordinals, as used in proof theory.

In this talk I discuss fundamental definitions and results, without assuming any prerequisites from proof theory. My aim is to explain the following recent theorem: By relativizing patterns of resemblance to dilators, one obtains an equivalence with Pi^1_1-comprehension, a central principle from reverse mathematics (arXiv:2012.10292).

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