2 problems

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Gaifman's end-extensional type conjecture for finite distributive lattices with a unique atom
Gaifman's conjecture. For every completion $T$ of $\mathsf{PA}$ and every finite distributive lattice $D$ with a unique atom, there is an end-extensional type $p(x)$ of $T$ that pr…
Conjecturesolvedlattice-theory models-of-pa model-theoryarXiv posted 2 days ago
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Gaifman's lattice-realization conjecture for finite distributive lattices
Gaifman's conjecture. For every finite distributive lattice $D$ and every model $d4a0$ , there is an elementary end extension $d4a1$ of $d4a0$ such that
Conjecturesolvedlattice-theory models-of-pa model-theoryarXiv posted 2 days ago

Gaifman's end-extensional type conjecture for finite distributive lattices with a unique atom