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1. • CommentRowNumber1.
   • CommentAuthorzskoda
   • CommentTimeMay 25th 2012
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   Author: zskoda
   Format: MarkdownItexStub [[constructible set]], not yet precise (e.g. the universe is not a Boolean algebra as it is a proper class), but gives idea what we could work on in the entry.

   Stub constructible set, not yet precise (e.g. the universe is not a Boolean algebra as it is a proper class), but gives idea what we could work on in the entry.

2. • CommentRowNumber2.
   • CommentAuthorTobyBartels
   • CommentTimeMay 29th 2012
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   Author: TobyBartels
   Format: MarkdownItexThe class of pure sets is a *large* Boolean algebra, so I wouldn't worry about that. But I don't understood how the constructible universe is analogous to the Borel algebra of a topological space. (And in the latter case, wouldn't one just say "Borel set" instead of "constructible set"?) Perhaps the algebraic geometry provides the link? (Clearly you've barely touched on that.)

   The class of pure sets is a large Boolean algebra, so I wouldn’t worry about that. But I don’t understood how the constructible universe is analogous to the Borel algebra of a topological space. (And in the latter case, wouldn’t one just say “Borel set” instead of “constructible set”?) Perhaps the algebraic geometry provides the link? (Clearly you’ve barely touched on that.)

3. • CommentRowNumber3.
   • CommentAuthorzskoda
   • CommentTimeMay 29th 2012
   • (edited May 29th 2012)
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   Author: zskoda
   Format: MarkdownItexThanks, Toby. No, Toby, I WAS ENTIRELY WRONG. Borel sets are much more general than constructible, sorry. The constructible sets in a topological space context form the smallest Boolean subalgebra containing open sets. I should correct this. In any case, both notions are central in the part of model theory which is called 'descriptive set theory'.

   Thanks, Toby.

   No, Toby, I WAS ENTIRELY WRONG. Borel sets are much more general than constructible, sorry. The constructible sets in a topological space context form the smallest Boolean subalgebra containing open sets. I should correct this.

   In any case, both notions are central in the part of model theory which is called ’descriptive set theory’.

4. • CommentRowNumber4.
   • CommentAuthorTobyBartels
   • CommentTimeMay 30th 2012
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   Author: TobyBartels
   Format: MarkdownItexI see, you wrote "Borel" where it should be (and now is) "Boolean". Now it makes sense (including the word "smallest"). I still don't see the connection to Gödel constructibility, other than the very general notion of definability in some language over some objects (in one case, the language of boolean algebra over the open sets; in the other case, the language of material set theory over the von Neumann ordinals). Is there a more precise analogy than this?

   I see, you wrote “Borel” where it should be (and now is) “Boolean”. Now it makes sense (including the word “smallest”).

   I still don’t see the connection to Gödel constructibility, other than the very general notion of definability in some language over some objects (in one case, the language of boolean algebra over the open sets; in the other case, the language of material set theory over the von Neumann ordinals). Is there a more precise analogy than this?