Timeline for Is there a notion analogous to separability but requiring definable rather than countable sets?
Current License: CC BY-SA 3.0
14 events
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| Dec 24, 2014 at 23:10 | comment | added | fritzo | @PaulTaylor Thanks, I changed 'compactness' to 'separability' in title and gave an example in Real numbers. I'm struggling to frame the question without tying too closely to a single domain. | |
| Dec 24, 2014 at 23:03 | history | edited | fritzo | CC BY-SA 3.0 |
Make related properties more precise
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| Dec 24, 2014 at 22:58 | history | edited | fritzo | CC BY-SA 3.0 |
Make related properties more precise
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| Dec 24, 2014 at 22:53 | history | edited | fritzo | CC BY-SA 3.0 |
Reword title to use 'separability' instead of 'compactness'
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| Dec 24, 2014 at 22:21 | history | edited | fritzo | CC BY-SA 3.0 |
edited title
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| Dec 24, 2014 at 20:19 | comment | added | Paul Taylor | Besides containing a spelling mistake, your title is misleading about your question. | |
| Dec 24, 2014 at 20:18 | comment | added | Paul Taylor | You're asking that the finite or compact elements of the model be definable. This is one of the requirements for full abstraction; maybe Basil's suggested article by Curien might help you with this. Unfortunately, a lot of the theoretical computer scientists who might have answered this question have now left MathOverflow for another site. | |
| Dec 24, 2014 at 17:31 | comment | added | fritzo | @Basil Thanks for the reference. Here are three "definability"-like properties: a model is definable if it can be constructed in some language; a model is "definably inhabited" if each of its elements is definable (e.g. the rationals or the algebraic reals, depending on language); and a model is "definably compact" if each of its elements is a sup of definable elements (e.g. the standard reals or the Bohm tree model). It is this last property I am interested in. | |
| Dec 24, 2014 at 17:24 | history | edited | fritzo | CC BY-SA 3.0 |
added 73 characters in body
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| Dec 24, 2014 at 11:38 | comment | added | Basil | People in higher-order computability also say "recursive in f, g..." for an element definable by abstractions, applications, initial functions and fixpoints over extra (e.g. parallel) elements f, g... | |
| Dec 24, 2014 at 11:27 | comment | added | Basil | Why not just "definability"? These matters are related to the concept of "sequentiality" as well. This light article by Curien might help. | |
| Dec 24, 2014 at 5:21 | history | edited | fritzo | CC BY-SA 3.0 |
change tags
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| Dec 24, 2014 at 5:11 | history | edited | fritzo | CC BY-SA 3.0 |
fix grammar
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| Dec 23, 2014 at 23:08 | history | asked | fritzo | CC BY-SA 3.0 |