Natural sequences of extensions Fn aligned with standard logical hierarchies

Construct and justify natural sequences of conservative extensions {Fn} over a base system F0 that correspond to common hierarchies in logic, such as the reverse mathematics progression (e.g., RCA0, ACA0, ATR0, ...) or hierarchies used in proof assistants, and demonstrate that these sequences yield coherent stratifications of definability within the fractal countability framework.

Background

The framework emphasizes that S∞ depends on the choice of base system F0 and the sequence of conservative extensions {Fn}. Earlier sections connect particular choices (e.g., RCA0→ACA0→ATR0) to standard hierarchies, illustrating how S∞ can recover familiar classes such as HYP.

A central methodological question is whether there are canonical—or at least widely acceptable—ways to choose {Fn} that align with established hierarchies in reverse mathematics or with type-theoretic layers implemented in proof assistants, thereby providing principled, reproducible stratifications of definability.