2 problems

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Non-finite basis conjecture for the variety of MV-monoidal algebras
Non-finite basis conjecture. The variety generated by this algebra is not finitely based; in particular, the variety of $\mathsf{MVM}$ -algebras is not generated by $[0,1]$ . This is…
Conjectureopenlattice-ordered-monoids mv-algebras universal-algebraarXiv posted 2 days ago
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The unit-cube Pierce–Birkhoff conjecture
Let $PWP(n)_u$ be the set of continuous piecewise-polynomial functions from $[0,1]^n$ to $[0,1]$ , let $ISD(n)_u$ be the set of continuous functions on $[0,1]^n$ expressible as fini…
Conjectureopenmv-algebras piecewise-polynomial-functions pierce-birkhoff-conjecturearXiv posted 2 days ago

Non-finite basis conjecture for the variety of MV-monoidal algebras