4 problems

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Dawar's fixed-point definability conjecture for finite rigid structures
Dawar's conjecture. For every finitely axiomatizable class $K$ of rigid structures, some formula in the fixed-point extension of first-order logic defines a linear order in $K$ .
Conjectureopenfinite-model-theory finite-structures fixed-point-logicarXiv posted 2 days ago
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McColm's conjecture on bounded positive elementary inductions
McColm's conjecture. If every $(\operatorname{FO}+\operatorname{LFP})$ formula is equivalent to a first-order formula in $K$ , then every positive elementary induction is bounded in…
Conjectureopenfinite-model-theory finite-structures fixed-point-logicarXiv posted 2 days ago
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Schmitz's path characterization of labelled well-quasi-orderings
Schmitz's conjecture. The following are equivalent: (i) the class of structures in $\mathcal{C}$ labelled with any well-quasi-ordered set $(Y,\leq)$ is itself well-quasi-ordered un…
Conjectureopenfinite-structures model-theory well-quasi-orderingsarXiv posted 2 days ago
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The EPPA–Ramsey expansion conjecture
EPPA–Ramsey expansion conjecture. Every class with EPPA has a precompact Ramsey expansion.
Conjectureopeneppa finite-structures ramsey-theoryarXiv posted 2 days ago

Dawar's fixed-point definability conjecture for finite rigid structures