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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.05841 |
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Table of Contents:
- Birkhoff's representation theorem for finite distributive lattices states that any finite distributive lattice is isomorphic to the lattice of order ideals (lower sets) of the partial order of the join-irreducible elements of the lattice. We present a simplified version of Stone's extension of this theorem to general distributive lattices. We then apply this formulation to locally finite distributive lattices to produce a novel representation theorem: The lattice is isomorphic to the order ideals of the poset of prime filters of the lattice whose symmetric difference from a particular ideal is finite.