A model is constructed in which boldface Σ¹₃-uniformization holds while lightface Σ¹₄-uniformization fails, separating the two principles.
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math.LO 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Proves consistency of ZFC model in which graphs of all total Π¹₃-functions are Σ¹₃, incompatible with Π¹₃-uniformization.
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On $\boldsymbol{\Sigma}^1_3$- and $\Sigma^1_4$-uniformization
A model is constructed in which boldface Σ¹₃-uniformization holds while lightface Σ¹₄-uniformization fails, separating the two principles.
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On graphs of total projective functions
Proves consistency of ZFC model in which graphs of all total Π¹₃-functions are Σ¹₃, incompatible with Π¹₃-uniformization.