Foundations of Online Structure Theory II: The Operator Approach

We introduce a framework for online structure theory. Our approach generalises notions arising independently in several areas of computability theory and complexity suggest unifying using operators where we allow the input to be countable object an arbitrary complexity. give new which (i) ties algorithms with computable analysis, (ii) shows how use modifications from such as Weihrauch reducibility, analyse finite but uniform combinatorics, (iii) show finitize reverse mathematics fine analogs infinite combinatorial problems, (iv) see similar ideas can amalgamated EX-learning, distributed computing like. One key is that viewed sub-area analysis. Conversely, also get enrichment analysis classical algorithms.