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Explore the foundational concepts of Strict Reverse Mathematics (SRM) in this mathematical lecture delivered at the Erwin Schrödinger International Institute. Learn about Harvey Friedman's original conception of Reverse Mathematics, which requires either no base theory at all or demands that every statement in the base theory be strictly mathematical in its own right. Discover how SRM differs from traditional Reverse Mathematics and examine the systematic reuse of fundamental strictly mathematical statements. Investigate the logical equivalence between RCA_0 and the Elementary Theory of Functions (ETF), a claim originally made in founding Journal of Symbolic Logic abstracts but left undocumented until recent work. Understand the challenges involved in developing SRM into a systematically vibrant subject comparable to traditional Reverse Mathematics, and review current state-of-the-art developments in upgrading and extending foundational results in this emerging field of mathematical logic.
