On graphs of total projective functions

Stefan Hoffelner

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arXiv · 2605.21184

On graphs of total projective functions

Stefan Hoffelner

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Abstract

It is well known that the graph of a total $\mathbf{\Sigma}^1_n$-function is $\mathbf{\Pi}^1_n$. We prove the consistency of the dual assertion at the third projective level: there is a model of $\ZFC$ in which the graph of every total $\mathbf{\Pi}^1_3$-function is $\mathbf{\Sigma}^1_3$. This principle is incompatible with $\mathbf{\Pi}^1_3$-uniformization and hence with the usual projective-determinacy picture. The construction also repairs the final step of the failure-of-uniformization argument from~\cite{HOFFELNER2023103292}.

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Stefan Hoffelner. 2026-05-20. On graphs of total projective functions. https://arxiv.org/abs/2605.21184

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