Abstract:

Well ordering principles are statements of the form ``F(X) is a well order for any well order X", where F is a transformation of linear orders (usually computable). They connect several areas of mathematical logic, notably ordinal analysis, computability theory and reverse mathematics. In this talk, I introduce the area and present recent work with Michael Rathjen and Andreas Weiermann (arXiv:2001.06380): We have investigated the astonishing meta-mathematical properties of a uniform Kruskal theorem, which extends the original theorem from trees to general recursive data types.