Questions tagged [constructive-mathematics]
Constructive mathematics in the style of Bishop, including its semantics using realizabilty or topological methods.
3 questions from the last 30 days
3
votes
1
answer
375
views
Injective envelopes, constructively?
Question 0:
How do injective envelopes work in constructive mathematics?
For example,
Question 1: How strong is it to assert internally that there are enough injectives (in the category of sets, say)? ...
- 68.1k
15
votes
0
answers
524
views
What is the relation between the constructive Hilbert basis theorem and the theory of Gröbner bases?
Gröbner bases are often praised for their effectiveness in providing algorithmic solutions to problems in commutative algebra which a priori don't have an obvious computational solution.
For example, ...
- 1,816
9
votes
0
answers
109
views
Does $\mathsf{IZF}_{\mathrm{Rep}}$ prove that $L_{\omega_1^{\mathrm{CK}}}$ is a model of $\mathsf{IKP}$ (with $\Sigma_0$-collection)?
Let $\def\IZF{\mathsf{IZF}_{\mathrm{Rep}}}\IZF$ be intuitionistic Zermelo-Fraenkel set theory with the replacement scheme. (See this SEP article for a definition of the replacement scheme.) Let $\def\...
- 21.4k