## New answers tagged constructive-mathematics

3
votes

### Weakest theory over which "all sets are measurable" has consistency strength?

This is more of an extended comment than an answer, but I think it's an important point to make. Also, as I discuss at the end it is technically an answer.
You are never going to have a constructively ...

6
votes

Accepted

### Does negative trichotomy hold for constructive ordinals?

I'll assume by ordinal you mean a set with a transitive, well-founded, and extensional relation. Then it's not constructively valid that $\neg \neg (A < B \vee A = B \vee A > B)$ for ordinals $A$...

2
votes

### Does negative trichotomy hold for constructive ordinals?

It's three decades since I wrote Intuitionistic Sets and Ordinals, at which time I knew how to express well founded relations as coalgebras, but I had very little understanding of the subject.
In ...

6
votes

Accepted

### In the constructive theory of direct categories, is it decidable whether an arbitrary morphism is an identity or not?

I believe (2) is the best definition. Consider what you want to do with a direct category: you want to construct presheaves and natural transformations between them inductively, assuming that they ...

4
votes

### In the constructive theory of direct categories, is it decidable whether an arbitrary morphism is an identity or not?

To ask whether it is decidable if a morphism is an identity is the wrong question here. In any more general setting the answer to this ought to be "no", however, here we don't have any non-...

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