Iterated Graph Derivatives, Antiderivatives, and Priority Arguments

Explore the mathematical concepts of iterated graph derivatives and antiderivatives through this 41-minute conference talk that extends classical results from linear orders to graphs, trees, and forests. Learn how the Hausdorff derivative of a linear order can be iterated to ordinal length, creating sequences of quotient linear orders where each step requires a double jump calculation. Discover the Ash and Watnick converse theorem involving antiderivatives as product orderings of lower complexity than original orderings. Examine a novel variant motivated by uncountable computability theory where derivatives become substructures rather than quotient structures, with applications extending beyond linear orders to include graphs, trees, and forests. Understand how priority arguments factor into these mathematical constructions, with primary focus on countable graphs and computability theory while incorporating insights from other mathematical structures and uncountable computability theory.