The Borel directed graphs with dichromatic number at least 3 form a Π¹₂-complete class, so no countable basis exists under Borel homomorphisms.
Kechris, Sławomir Solecki, and Stevo Todor c evi \'c
2 Pith papers cite this work. Polarity classification is still indexing.
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math.LO 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
A concise proof of the L0 dichotomy is obtained by adapting Bernshteyn's framework for G0, using a sigma-ideal of small homomorphism sets defined by bounded odd-walk conditions and proved via the First Reflection Theorem.
citing papers explorer
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No Countable Basis for Borel Directed Graphs of Dichromatic Number at Least Three
The Borel directed graphs with dichromatic number at least 3 form a Π¹₂-complete class, so no countable basis exists under Borel homomorphisms.
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A Concise Proof of the $L_0$ Dichotomy
A concise proof of the L0 dichotomy is obtained by adapting Bernshteyn's framework for G0, using a sigma-ideal of small homomorphism sets defined by bounded odd-walk conditions and proved via the First Reflection Theorem.