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A set $X\subseteq\omega^\omega$ is unravelable iff there is a possibly larger set $A$ and a clopen set $Y\subseteq A^\omega$ (with respect to the product topology coming from the discrete topology on $A$) such that winning strategies for the game on $A$ with payoff set $Y$ can be converted to winning strategies for the game on $\omega$ with payoff set $X$ in a particularly simple way (see Martin - A purely inductive proof of Borel determinacy for the precise definition). By Gale–Stewart, unravelability implies determinacy; however, it is not the only route to proving the determinacy of a pointclass.

My question is whether there is a known upper bound on the complexity of an unravelable pointclass. To make this somewhat precise:

Is it consistent with $\mathsf{ZFC}$ that every set in $\mathcal{P}(\mathbb{R})^{L(\mathbb{R})}$ is unravelable?

The strongest results I can find are vastly weaker than this, namely that under large cardinal assumptions $\Pi^1_1$ sets are unravelable (Neeman 1,2; I remember seeing the same result for Borel-on-$\Pi^1_1$ sets, but I can't find a reference for it at the moment). On the other hand, I don't see an easy proof that this is anywhere close to the most unravelability we can expect, nor can I find this stated in the literature.

A set $X\subseteq\omega^\omega$ is unravelable iff there is a possibly larger set $A$ and a clopen set $Y\subseteq A^\omega$ (with respect to the product topology coming from the discrete topology on $A$) such that winning strategies for the game on $A$ with payoff set $Y$ can be converted to winning strategies for the game on $\omega$ with payoff set $X$ in a particularly simple way (see Martin's paper A purely inductive proof of Borel determinacy for the precise definition). By Gale–Stewart, unravelability implies determinacy; however, it is not the only route to proving the determinacy of a pointclass.

My question is whether there is a known upper bound on the complexity of an unravelable pointclass. To make this somewhat precise:

Is it consistent with $\mathsf{ZFC}$ that every set in $\mathcal{P}(\mathbb{R})^{L(\mathbb{R})}$ is unravelable?

The strongest results I can find are vastly weaker than this, namely that under large cardinal assumptions $\Pi^1_1$ sets are unravelable (Neeman 1,2; I remember seeing the same result for Borel-on-$\Pi^1_1$ sets, but I can't find a reference for it at the moment). On the other hand, I don't see an easy proof that this is anywhere close to the most unravelability we can expect, nor can I find this stated in the literature.

A set $X\subseteq\omega^\omega$ is unravelable iff there is a possibly larger set $A$ and a clopen set $Y\subseteq A^\omega$ (with respect to the product topology coming from the discrete topology on $A$) such that winning strategies for the game on $A$ with payoff set $Y$ can be converted to winning strategies for the game on $\omega$ with payoff set $X$ in a particularly simple way (see Martin - A purely inductive proof of Borel determinacy for the precise definition). By Gale–Stewart, unravelability implies determinacy; however, it is not the only route to proving the determinacy of a pointclass.

My question is whether there is a known upper bound on the complexity of an unravelable pointclass. To make this somewhat precise:

Is it consistent with $\mathsf{ZFC}$ that every set in $\mathcal{P}(\mathbb{R})^{L(\mathbb{R})}$ is unravelable?

The strongest results I can find are vastly weaker than this, namely that under large cardinal assumptions Borel-on-$\Pi^1_1$ sets are unravelable. On the other hand, I don't see an easy proof that this is the most unravelability we can expect, nor can I find this stated in the literature.

A set $X\subseteq\omega^\omega$ is unravelable iff there is a possibly larger set $A$ and a clopen set $Y\subseteq A^\omega$ (with respect to the product topology coming from the discrete topology on $A$) such that winning strategies for the game on $A$ with payoff set $Y$ can be converted to winning strategies for the game on $\omega$ with payoff set $X$ in a particularly simple way (see Martin - A purely inductive proof of Borel determinacy for the precise definition). By Gale–Stewart, unravelability implies determinacy; however, it is not the only route to proving the determinacy of a pointclass.

My question is whether there is a known upper bound on the complexity of an unravelable pointclass. To make this somewhat precise:

Is it consistent with $\mathsf{ZFC}$ that every set in $\mathcal{P}(\mathbb{R})^{L(\mathbb{R})}$ is unravelable?

The strongest results I can find are vastly weaker than this, namely that under large cardinal assumptions $\Pi^1_1$ sets are unravelable (Neeman 1,2; I remember seeing the same result for Borel-on-$\Pi^1_1$ sets, but I can't find a reference for it at the moment). On the other hand, I don't see an easy proof that this is anywhere close to the most unravelability we can expect, nor can I find this stated in the literature.

A set $X\subseteq\omega^\omega$ is unravelable iff there is a possibly larger set $A$ and a clopen set $Y\subseteq A^\omega$ (with respect to the product topology coming from the discrete topology on $A$) such that winning strategies for the game on $A$ with payoff set $Y$ can be converted to winning strategies for the game on $\omega$ with payoff set $X$ in a particularly simple way (see here for the precise definition). By Gale-Stewart, unravelability implies determinacy; however, it is not the only route to proving the determinacy of a pointclass.

My question is whether there is a known upper bound on the complexity of an unravelable pointclass. To make this somewhat precise:

Is it consistent with $\mathsf{ZFC}$ that every set in $\mathcal{P}(\mathbb{R})^{L(\mathbb{R})}$ is unravelable?

The strongest results I can find are vastly weaker than this, namely that under large cardinal assumptions Borel-on-$\Pi^1_1$ sets are unravellable. On the other hand, I don't see an easy proof that this is the most unravellability we can expect, nor can I find this stated in the literature.

A set $X\subseteq\omega^\omega$ is unravelable iff there is a possibly larger set $A$ and a clopen set $Y\subseteq A^\omega$ (with respect to the product topology coming from the discrete topology on $A$) such that winning strategies for the game on $A$ with payoff set $Y$ can be converted to winning strategies for the game on $\omega$ with payoff set $X$ in a particularly simple way (see Martin - A purely inductive proof of Borel determinacy for the precise definition). By Gale–Stewart, unravelability implies determinacy; however, it is not the only route to proving the determinacy of a pointclass.

My question is whether there is a known upper bound on the complexity of an unravelable pointclass. To make this somewhat precise:

Is it consistent with $\mathsf{ZFC}$ that every set in $\mathcal{P}(\mathbb{R})^{L(\mathbb{R})}$ is unravelable?

The strongest results I can find are vastly weaker than this, namely that under large cardinal assumptions Borel-on-$\Pi^1_1$ sets are unravelable. On the other hand, I don't see an easy proof that this is the most unravelability we can expect, nor can I find this stated in the literature.