I've been surfing the internet, and have found some subsystems or additional axioms of second-order arithmetic whose definitions I could not find. Does anyone know what the following axioms/subsystems are?
- $\beta$-model reflection
- Lightface comprehension (e.g. lightface $\Pi^1_2$-comprehension)
- CR (e.g. $\Delta^1_1$-CR, I do not know what CR stands for)
- Bar recursion (the Wikipedia article for it seems unrelated and confusing)