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1. • CommentRowNumber1.
   • CommentAuthorporton
   • CommentTimeDec 23rd 2014
   • (edited Dec 23rd 2014)
   • PermaLink
   Author: porton
   Format: MarkdownItexIt seems that I've proved that every atomistic poset is a co-brouwerian lattice. The proof is an easy generalization of my theorem 6.86 in my draft book: [My book draft](http://www.mathematics21.org/binaries/volume-1.pdf) Is it true? (in other words, there is no error in my proof?) Please confirm the correctness of my result before we edit and include this result into [nLab article](http://nlab.mathforge.org/nlab/show/atom) Should we also edit [Wikipedia](https://en.wikipedia.org/wiki/Atom_%28order_theory%29) to include this fact? (If yes, which reference to cite?)

   It seems that I’ve proved that every atomistic poset is a co-brouwerian lattice.

   The proof is an easy generalization of my theorem 6.86 in my draft book:

   My book draft

   Is it true? (in other words, there is no error in my proof?)

   Please confirm the correctness of my result before we edit and include this result into nLab article

   Should we also edit Wikipedia to include this fact? (If yes, which reference to cite?)

2. • CommentRowNumber2.
   • CommentAuthorTodd_Trimble
   • CommentTimeDec 23rd 2014
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexIt's not true. For example, a typical [geometric lattice](http://en.wikipedia.org/wiki/Geometric_lattice) such as the lattice of equivalence relations on a finite set is not even distributive, much less co-brouwerian (meaning, I presume, opposite to a Heyting algebra).

   It’s not true. For example, a typical geometric lattice such as the lattice of equivalence relations on a finite set is not even distributive, much less co-brouwerian (meaning, I presume, opposite to a Heyting algebra).

3. • CommentRowNumber3.
   • CommentAuthorporton
   • CommentTimeDec 23rd 2014
   • PermaLink
   Author: porton
   Format: MarkdownItexOh, I see. My proof uses features specific to funcoids and does not generalize for other atomistic lattices. Sorry for your time spend about a non-existent generalization of my proof. (The proof itself is correct, just it cannot be generalized.)

   Oh, I see. My proof uses features specific to funcoids and does not generalize for other atomistic lattices.

   Sorry for your time spend about a non-existent generalization of my proof. (The proof itself is correct, just it cannot be generalized.)