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Atrium > Mathematics, Physics & Philosophy: Properties of free join-semilattices

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- CommentRowNumber1.
- CommentAuthorporton
- CommentTimeDec 26th 2015
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Author: porton
Format: MarkdownItexI want to know properties of free join-semilattices (generated by infinite sets in the general case). For example, are such semi-lattices distributive, complete, atomic, atomistic, etc.?

I want to know properties of free join-semilattices (generated by infinite sets in the general case).

For example, are such semi-lattices distributive, complete, atomic, atomistic, etc.?
- CommentRowNumber2.
- CommentAuthorMike Shulman
- CommentTimeDec 27th 2015
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Author: Mike Shulman
Format: MarkdownItexUnless I'm mistaken, the free join-semilattice on $A$ is the poset of finite subsets of $A$. So it has inhabited meets that distribute over its finite joins, but it is not complete.

Unless I’m mistaken, the free join-semilattice on $A$ is the poset of finite subsets of $A$ . So it has inhabited meets that distribute over its finite joins, but it is not complete.

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