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Explore the advanced concepts of Strict Reverse Mathematics (SRM) in this 52-minute conference 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 Learn about the logical equivalence between RCA_0 and the Elementary Theory of Functions (ETF), a claim originally made in founding JSL abstracts but left undocumented until recent work. Discover the systematic reuse of fundamental strictly mathematical statements and examine results from manuscript #116 that demonstrate progress in developing SRM. Understand the challenges involved in transforming SRM into a systematically vibrant subject comparable to traditional Reverse Mathematics, and gain insights into current state-of-the-art developments in upgrading and extending these foundational concepts.
