No finite axiomatizations for posets embeddable into distributive lattices

Abstract

Let $m$ and $n$ be cardinals with $3\le m,n\le \omega$. We show that the class of posets that can be embedded into a distributive lattice via a map preserving all existing meets and joins with cardinalities strictly less than $m$ and $n$ respectively cannot be finitely axiomatized.

Revised versions make minor changes to the exposition in some places

References in corpus (2)

• Representable posets
• Non-elementary classes of representable posets

Cited by in corpus (3)

• Recursive axiomatizations for representable posets
• Closure operators, frames, and neatest representations
• Recursive axiomatisations from separation properties