User Madeleine Birchfield

64 votes

6 answers

52k views

Consequences of Kirti Joshi's new preprint about p-adic Teichmüller theory on the validity of IUT and on the ABC conjecture

asked Nov 22, 2022 at 12:32

11 votes

1 answer

1k views

In the rational numbers, is every convergent power series a Taylor series for a rational function?

asked Sep 7, 2022 at 16:49

10 votes

2 answers

1k views

Proof in constructive mathematics that the principal square root function exists in any Cauchy complete Archimedean ordered field

asked Jul 6, 2022 at 2:19

10 votes

1 answer

580 views

Universal property of the set of injections in the category of sets

asked Jan 10, 2023 at 6:52

9 votes

0 answers

4k views

Is there a mistake in Mochizuki's proof of Theorem 1.10 in IUTT IV? [closed]

asked Mar 31 at 11:56

9 votes

3 answers

1k views

Axioms for the category of groups

asked Oct 22, 2022 at 0:45

8 votes

1 answer

373 views

Status of the fundamental theorem of algebra for the locale of real numbers

asked Nov 21, 2022 at 16:51

8 votes

1 answer

258 views

Sequential colimit of iterated quotients of Cauchy sequences

asked Oct 3, 2023 at 3:48

7 votes

1 answer

290 views

Equivalence of omniscience principles for natural numbers and analytic omniscience principles for Cauchy real numbers

asked Jul 6 at 20:28

7 votes

1 answer

310 views

Does a tight apartness relation on a subobject classifier imply the elementary topos is Boolean?

asked Mar 11, 2023 at 0:59

6 votes

1 answer

289 views

Archimedean ordered fields without maxima and minima in constructive mathematics

asked Feb 7 at 18:39

6 votes

0 answers

108 views

Archimedean ordered field in which every function is smooth

asked Feb 8 at 13:16

6 votes

1 answer

157 views

Univalence for weakly Tarski universes

asked Oct 4, 2022 at 1:15

6 votes

1 answer

338 views

Proper definition of ordered field in constructive mathematics

asked Jul 5, 2022 at 18:12

5 votes

3 answers

556 views

The field structure on the locale of real numbers

asked Nov 16, 2022 at 13:15

5 votes

0 answers

158 views

Weaker versions of the Riemann series theorem in constructive mathematics

asked Jan 4, 2023 at 22:23

5 votes

1 answer

171 views

Are lists in homotopy type theory free $A_\infty$-spaces?

asked Jan 24, 2023 at 14:55

4 votes

1 answer

170 views

Constructing coproduct types and boolean types from universes

asked Nov 7, 2023 at 2:13

4 votes

1 answer

442 views

$(n,1)$-dagger categories

asked Jul 25, 2022 at 23:02

4 votes

1 answer

262 views

Constructing ordered fields with lattice structure from ordered fields without lattice structure, and vice versa, in constructive mathematics

asked Jul 5, 2022 at 19:25

4 votes

1 answer

377 views

Codependent types in type theory

asked Jun 3, 2022 at 1:09

4 votes

1 answer

192 views

Predicativity and axiom $\mathbb{R}\flat$ in real cohesive homotopy type theory

asked Jun 10, 2022 at 5:33

4 votes

1 answer

376 views

Equivalence of real numbers in terms of Dedekind cuts and Cauchy nets of rational numbers

asked Jul 13, 2022 at 0:17

3 votes

0 answers

74 views

Discreteness of the higher inductive-inductive Cauchy real numbers in real cohesive homotopy type theory

asked Jul 16, 2022 at 21:15

3 votes

0 answers

292 views

Principle of unique choice in homotopy type theory

asked Jul 6, 2022 at 4:07

3 votes

1 answer

115 views

Analogue of Kock-Lawvere axiom for power series rings?

asked Jan 13, 2023 at 7:19

2 votes

1 answer

570 views

Higher inductive types in higher observational type theory

asked Jul 18, 2022 at 23:33

2 votes

1 answer

477 views

Path types and identity types in dependent type theory

asked Sep 3, 2022 at 21:37

1 vote

0 answers

76 views

Directly proving the extensionality principle for product types without quasi-inverses

asked Dec 18, 2022 at 21:33

1 vote

1 answer

75 views

Constructing set-truncations of types from universes

asked Nov 10, 2023 at 10:31

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31 Questions

Consequences of Kirti Joshi's new preprint about p-adic Teichmüller theory on the validity of IUT and on the ABC conjecture

In the rational numbers, is every convergent power series a Taylor series for a rational function?

Proof in constructive mathematics that the principal square root function exists in any Cauchy complete Archimedean ordered field

Universal property of the set of injections in the category of sets

Is there a mistake in Mochizuki's proof of Theorem 1.10 in IUTT IV? [closed]

Axioms for the category of groups

Status of the fundamental theorem of algebra for the locale of real numbers

Sequential colimit of iterated quotients of Cauchy sequences

Equivalence of omniscience principles for natural numbers and analytic omniscience principles for Cauchy real numbers

Does a tight apartness relation on a subobject classifier imply the elementary topos is Boolean?

Archimedean ordered fields without maxima and minima in constructive mathematics

Archimedean ordered field in which every function is smooth

Univalence for weakly Tarski universes

Proper definition of ordered field in constructive mathematics

The field structure on the locale of real numbers

Weaker versions of the Riemann series theorem in constructive mathematics

Are lists in homotopy type theory free $A_\infty$-spaces?

Constructing coproduct types and boolean types from universes

$(n,1)$-dagger categories

Constructing ordered fields with lattice structure from ordered fields without lattice structure, and vice versa, in constructive mathematics

Codependent types in type theory

Predicativity and axiom $\mathbb{R}\flat$ in real cohesive homotopy type theory

Equivalence of real numbers in terms of Dedekind cuts and Cauchy nets of rational numbers

Discreteness of the higher inductive-inductive Cauchy real numbers in real cohesive homotopy type theory

Principle of unique choice in homotopy type theory

Analogue of Kock-Lawvere axiom for power series rings?

Higher inductive types in higher observational type theory

Path types and identity types in dependent type theory

Directly proving the extensionality principle for product types without quasi-inverses

Constructing set-truncations of types from universes