06/06/2022, 12:42 AM
If I'm not mistaken, Geisler's circulation coincides with what in the Rubtsov-Romerio's terminology call omegation.
These concepts are defined via limits-convergence.
Fast growing hierarchies, instead, are part of the study of subrecursive hierarchies of function, a segment of recursion theory that deals with refining the Grzegorczyk classification of primitive recursive functions using other kind of recursion schema built around ordinal sequences of "benchmark functions" extending Ackermann-like ones.
We can say that this can be seen as an extension of the theory of goodstein maps from natural ranks to countable-ordinal ranks \(\alpha<\omega_1\).
Also the FGH are constructions used in the study of definability, a part of recursion theory/computation theory: in particular in the form of ordinal notations and ordinal definability.
These concepts are defined via limits-convergence.
Fast growing hierarchies, instead, are part of the study of subrecursive hierarchies of function, a segment of recursion theory that deals with refining the Grzegorczyk classification of primitive recursive functions using other kind of recursion schema built around ordinal sequences of "benchmark functions" extending Ackermann-like ones.
We can say that this can be seen as an extension of the theory of goodstein maps from natural ranks to countable-ordinal ranks \(\alpha<\omega_1\).
Also the FGH are constructions used in the study of definability, a part of recursion theory/computation theory: in particular in the form of ordinal notations and ordinal definability.
Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)
\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)
