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Explore the advanced concepts of Strict Reverse Mathematics (SRM) in this mathematical lecture delivered at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into Harvey Friedman's original conception of Reverse Mathematics, examining SRM as either requiring no base theory at all or demanding that every statement in the base theory be strictly mathematical in its own right. Learn about the logical equivalence between RCA_0 and the Elementary Theory of Functions (ETF), a claim originally made in founding Journal of Symbolic Logic abstracts but left undocumented until recent work. Discover the systematic reuse of fundamental strictly mathematical statements and examine results from manuscript #116 that advance the field. Understand the challenges involved in developing SRM into a systematically vibrant subject comparable to traditional Reverse Mathematics, and gain insights into current efforts to upgrade and extend these foundational concepts. Follow the state-of-the-art developments in this more complex mathematical framework that builds upon the established foundations of Reverse Mathematics.
