Notations: Recall that $\omega_1$ is the first uncountable ordinal. Let $X$ be a Polish space (completely metrizable and separable) and $F(X)$ be the collection of all real-valued functions on $X.$

A function $\rho:F(X)\to \omega_1$ is called an ordinal rank. In other words, ordinal rank assigns an ordinal to a function, typically measuring complexity of the function.

In $1990,$Kechris and Louveau conducted an investigation on three types of ordinal ranks acting on the class of Baire Class $1$ functions on a compact metric space (recall that $f$ is Baire Class $1$ if it is a pointwise limit of a sequence of continuous functions).

The three ranks are separation rank (introduced by Bourgain), oscillation rank and convergence rank (introduced by Zalcwasser, Gillespie and Hurwicz). They measure complexity of the respective definition of Baire Class $1$ functions (Baire Class $1$ functions have three equivalent definitions).

$26$ years later ($2016$), Marton, Viktor and Zoltan generalised from compact metric space to Polish space and the three ranks to Baire Class $\xi$ functions where $\xi$ is any countable ordinal (Recall that $f$ is Baire class $\xi$ if it is a pointwise limit of a sequence of Baire Class $\xi_n$ functions where $\xi_n<\xi$ for all natural number $n$). One of the generalisations is through topology refinement (For interested reader, please refer to section $5$ of their paper).

Question: Does there exist a literature on ordinal rank? More precisely, where can I find more information about ordinal rank?

Notations: Recall that $\omega_1$ is the first uncountable ordinal. Let $X$ be a Polish space (completely metrizable and separable) and $F(X)$ be the collection of all real-valued functions on $X.$

A function $\rho:F(X)\to \omega_1$ is called an ordinal rank. In other words, ordinal rank assigns an ordinal to a function, typically measuring complexity of the function.

In $1990,$Kechris and Louveau conducted an investigation on three types of ordinal ranks acting on the class of Baire Class $1$ functions on a compact metric space (recall that $f$ is Baire Class $1$ if it is a pointwise limit of a sequence of continuous functions).

The three ranks are separation rank (introduced by Bourgain), oscillation rank and convergence rank (introduced by Zalcwasser, Gillespie and Hurwicz). They measure complexity of the respective definition of Baire Class $1$ functions (Baire Class $1$ functions have three equivalent definitions).

$26$ years later ($2016$), Elekes, Kiss and Vidnyánszky generalised from compact metric space to Polish space and the three ranks to Baire Class $\xi$ functions where $\xi$ is any countable ordinal (Recall that $f$ is Baire class $\xi$ if it is a pointwise limit of a sequence of Baire Class $\xi_n$ functions where $\xi_n<\xi$ for all natural number $n$). One of the generalisations is through topology refinement (For interested reader, please refer to section $5$ of their paper).

Question: Does there exist a literature on ordinal rank? More precisely, where can I find more information about ordinal rank?

Notations: Recall that $\omega_1$ is the first uncountable ordinal. Let $X$ be a Polish space (completely metrizable and separable) and $F(X)$ be the collection of all real-valued functions on $X.$

A function $\rho:F(X)\to \omega_1$ is called an ordinal rank. In other words, ordinal rank assigns an ordinal to a function, typically measuring complexity of the function.

In $1990,$Kechris and Louveau conducted an investigation on three types of ordinal ranks acting on the class of Baire Class $1$ functions on a compact metric space (recall that $f$ is Baire Class $1$ if it is a pointwise limit of a sequence of continuous functions).

The three ranks are separation rank (introduced by Bourgain), oscillation rank and convergence rank (introduced by Zalcwasser, Gillespie and Hurwicz). They deal with the respective definition of Baire Class $1$ functions (Baire Class $1$ functions have three equivalent definitions).

$26$ years later ($2016$), Marton, Viktor and Zoltan generalised from compact metric space to Polish space and the three ranks to Baire Class $\xi$ functions where $\xi$ is any countable ordinal (Recall that $f$ is Baire class $\xi$ if it is a pointwise limit of a sequence of Baire Class $\xi_n$ functions where $\xi_n<\xi$ for all natural number $n$). One of the generalisations is through topology refinement (For interested reader, please refer to section $5$ of their paper).

Question: Does there exist a literature on ordinal rank? More precisely, where can I find more information about ordinal rank?

Notations: Recall that $\omega_1$ is the first uncountable ordinal. Let $X$ be a Polish space (completely metrizable and separable) and $F(X)$ be the collection of all real-valued functions on $X.$

A function $\rho:F(X)\to \omega_1$ is called an ordinal rank. In other words, ordinal rank assigns an ordinal to a function, typically measuring complexity of the function.

In $1990,$Kechris and Louveau conducted an investigation on three types of ordinal ranks acting on the class of Baire Class $1$ functions on a compact metric space (recall that $f$ is Baire Class $1$ if it is a pointwise limit of a sequence of continuous functions).

The three ranks are separation rank (introduced by Bourgain), oscillation rank and convergence rank (introduced by Zalcwasser, Gillespie and Hurwicz). They measure complexity of the respective definition of Baire Class $1$ functions (Baire Class $1$ functions have three equivalent definitions).

$26$ years later ($2016$), Marton, Viktor and Zoltan generalised from compact metric space to Polish space and the three ranks to Baire Class $\xi$ functions where $\xi$ is any countable ordinal (Recall that $f$ is Baire class $\xi$ if it is a pointwise limit of a sequence of Baire Class $\xi_n$ functions where $\xi_n<\xi$ for all natural number $n$). One of the generalisations is through topology refinement (For interested reader, please refer to section $5$ of their paper).

Question: Does there exist a literature on ordinal rank? More precisely, where can I find more information about ordinal rank?