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Yes.


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awarded  Curious
Feb
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awarded  Nice Answer
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awarded  Yearling
Aug
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comment What are authoritative publications regarding foundational mathematics?
+1 for a generic female mathematician. It helps! I'll just add that those standards exist so people can build things that work together without ad-hoc human communication/intervention, a solution unnecessary in math. Also, mathematicians are like implementations--how often are standards implemented exactly according to the specs? This variety/flexibility is good and efficient. If I want to know common or uncommon definitions, I sample the internet.
Dec
24
awarded  Yearling
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awarded  Nice Question
Sep
3
accepted How does Borelness overlap with definability, computability, or constructiveness?
Sep
3
comment How does Borelness overlap with definability, computability, or constructiveness?
Thank you, that makes much sense. I also had not seen the Louveau paper, and it looks very interesting.
Sep
3
comment How does Borelness overlap with definability, computability, or constructiveness?
[...cont] My interest is logic, the paper is focused narrowly on Borel reductions, and the structures that we work with are orders, groups, and measures. I think it's interesting to ask how things change when you require everything to be Borel instead of allowing arbitrary sets. But I currently know no reason for Borel equivalence relations being a field of study (and populated by logicians). Surely it is not by pure happenstance that people write papers specifically about the classification of Borel equivalence relations. These objects and their classification must be special in some way. No?
Sep
3
comment How does Borelness overlap with definability, computability, or constructiveness?
I have read somewhere else that Borel sets were invented/defined because they are more appropriate than open sets for some questions in topology. This would be motivation enough for my introducing them except that, in ~20 pages, I mention topology only in the definition of Borel sets. When we actually go looking for Borel reductions, the topology and metric are completely useless. What matters is getting back choice in some limited way, e.g., through the group action, hyperfiniteness, or smoothness, or looking at the measures to see if what we want is possible. [cont...]
Sep
2
comment How does Borelness overlap with definability, computability, or constructiveness?
So are the Borel sets the ones with the simplest descriptions, e.g., using only countable quantification? The motivation that I give will be vague. I just want it to not be grossly inaccurate.
Sep
2
revised How does Borelness overlap with definability, computability, or constructiveness?
added related question
Sep
2
asked How does Borelness overlap with definability, computability, or constructiveness?
Aug
31
comment How many weak/strong limit cardinals exist under different assumptions?
I was thinking incorrectly. When an operation returns a subset/subclass of its input, the size of the set returned doesn't tell you how many elements were excluded. Thanks for your answers.
Aug
31
comment How many weak/strong limit cardinals exist under different assumptions?
Pardon the vagueness, but I am trying to get a general feel for these structures. So it's the limits that are responsible for the size of all of these classes (ordinals, cardinals, weak-limit cardinals, etc.)? That is, there are few objects between limits relative to the number of limits? You can keep taking limits (of limits of limits...) and always have a proper class?
Aug
31
accepted How many weak/strong limit cardinals exist under different assumptions?
Aug
31
comment How many weak/strong limit cardinals exist under different assumptions?
So among weak limit cardinals, there are limit weak limit cardinals that are analogous to limit ordinals in the order of On?
Aug
31
comment How many weak/strong limit cardinals exist under different assumptions?
Does it make sense to think about the "order type" of the class of weak limit cardinals? I really am interested in the idea of somehow iterating through this class, i.e., starting at the least one and reaching them all by repeated application of some operation.
Aug
31
asked How many weak/strong limit cardinals exist under different assumptions?
Aug
29
comment What does the concept of computation actually mean?
To clarify for myself the distinction between your two types of knowledge, is it similar to the distinction between a formal language and the model that you interpret it to be talking about? That is, are there two separate structures here connected by a map? And the Tortoise's "failure" is in his map? That is, he has the premises as propositions in his theory and has interpreted them so that they are associated to objects in his model. However, his map is not such that the relations among the propositions in the theory are carried over to relations among the objects in the model?