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7 votes

Computability of infinite-dimensional vector space

Short answer The general answer is that computability is easy for locally compact spaces, doable for separable spaces, and hard for non-separable spaces. The short anwer for a particular example, na …
Andrej Bauer's user avatar
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9 votes

Formal representation of an abstraction hierarchy

You are working on your PhD. Saying "I am not well versed in $X$" is not an excuse. And if you're good, then saying "my advisor does not know $X$" is not an excuse either. You are using monoids where …
Andrej Bauer's user avatar
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5 votes

What is necessary and/or sufficient requirement for a subring of a field to be computable?

$\Sigma$-algebra. … Because $\nabla$ preserves products, it maps $\mathcal{A}$ to a $\Sigma$-algebra $\nabla \mathcal{A}$ in $\mathsf{Asm}$. …
Andrej Bauer's user avatar
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7 votes

Does an initial algebra for a class have to belong to the class itself?

Yes, the initial algebra is by definition one of the members of the class for which it is initial. You may however be interested in the category-theoretic concept of a limit. … The limit is like an initial algebra. …
Andrej Bauer's user avatar
  • 29.5k