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Mathematical Logic


Project leader: Anton Freund

Title: „Continuous Order Transformations: A Bridge Between Ordinal Analysis, Reverse Mathematics, and Combinatorics“

Information on GEPRIS (DFG):

Project description:
The following question is central for several branches of mathematical logic: Which axiom systems are strong enough to prove a given mathematical theorem? In addition to its intrinsic intellectual interest, an answer to this question does often yield further information about the theorem in question, for example on the quality of approximations or the complexity of algorithmic solutions.

Our project aims to deepen connections between two branches of mathematical logic, which are both concerned with the central question formulated above: ordinal analysis and reverse mathematics. As a bridge between the two approaches, we use continuous transformations (finite-type functionals) over the categories of partial and linear orders. This will allow us to answer the central question in cases where it is currently open. Specifically, we want to analyze theorems of combinatorics, mostly related to Kruskal's tree theorem, the graph minor theorem, and the theory of better quasi orders. We also aim at a general framework, in which known and new results can be explained in a uniform way.