The elementary theory of the Young-Fibonacci lattice is undecidable and non-finitely axiomatizable, and the lattice with a constant for 2 has the maximal definability property.
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Undecidability of the elementary theory of Young--Fibonacci lattice
The elementary theory of the Young-Fibonacci lattice is undecidable and non-finitely axiomatizable, and the lattice with a constant for 2 has the maximal definability property.