Reverse Mathematics
Calibrating proof strength via subsystems of second-order arithmetic.
Reverse Mathematics. Calibrating proof strength via subsystems of second-order arithmetic.
Foundations and canonical references
The standard treatments of reverse mathematics approach the subject from complementary angles. Simpson, Subsystems of Second Order Arithmetic (2009) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.
Open methodological questions for reverse mathematics include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2009Subsystems of Second Order Arithmeticsimpson-2009
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