User abo

13 votes

What axioms are used to prove Gödel's Incompleteness Theorems?

answered Jan 6, 2013 at 12:39

12 votes

Set theories without "junk" theorems?

answered Mar 11, 2012 at 15:10

11 votes

Essential reads in the philosophy of mathematics and set theory

answered Apr 18, 2012 at 5:40

11 votes

Lists as a foundation of mathematics

answered Oct 18, 2023 at 8:18

10 votes

Dedekind-Peano axioms, but numbers have at most one successor

answered Jan 20, 2023 at 23:00

7 votes

Is there any formal foundation to ultrafinitism?

answered Nov 29, 2012 at 6:45

6 votes

Accepted

Why Does Induction Prove Multiplication is Commutative?

answered Feb 19, 2013 at 20:55

6 votes

What advantage humans have over computers in mathematics?

answered Mar 15, 2016 at 21:31

5 votes

Can FPA really prove its consistency?

answered Jan 23, 2019 at 9:21

5 votes

Accepted

Relationship between first and second incompleteness theorems

answered Feb 29, 2016 at 8:03

5 votes

Why Does Induction Prove Multiplication is Commutative?

answered Feb 17, 2013 at 15:57

3 votes

In what sense does the sentence $\operatorname{con}(\mathsf{PA})$ "say" that $\mathsf{PA}$ is consistent?

answered Nov 23, 2023 at 22:41

3 votes

Accepted

How do you restrict the induction axiom in second (or higher) order logic?

answered Mar 27, 2012 at 5:56

3 votes

Subsystems of Peano arithmetic and incompleteness theorem

answered Feb 12, 2012 at 12:59

2 votes

Intuitive and/or philosophical explanation for set theory paradoxes

answered Apr 15, 2012 at 11:09

2 votes

One can earn nothing on the Brownian motion, true ?

answered Jun 2, 2013 at 19:09

2 votes

Which model of computation is "the best"?

answered Jul 16, 2015 at 20:33

2 votes

Physics and Church–Turing Thesis

answered Dec 16, 2012 at 12:24

2 votes

Even XOR Odd Infinities?

answered Jan 20, 2013 at 21:37

1 vote

Is there any straightforward way to substitute for Gaussian/Brownian assumptions in financial mathematics?

answered Mar 1, 2013 at 18:23

1 vote

Finite versions of Godel' s incompleteness

answered Jun 29, 2012 at 5:24

1 vote

History of Logic Development

answered Jan 18, 2012 at 19:09

1 vote

Can ZFC prove "false theorems", and still be consistent? (was "Junk Theorems" follow up)

answered Mar 13, 2012 at 6:54

1 vote

Can this weakish system of arithmetic express multiplication for second-sort numbers?

answered Dec 29, 2023 at 16:35

1 vote

Why is an internal proof of consistency satisfactory for some systems?

answered Nov 21, 2023 at 9:42

1 vote

The concept of duality

answered Dec 11, 2019 at 21:56

1 vote

Notable mathematics during World War II

answered Aug 29, 2021 at 21:48

0 votes

Can FPA really prove its consistency?

answered Feb 22, 2019 at 14:54

0 votes

Reference request: Minimal Axiomatizations of PA over (+,x,<=).

answered May 19, 2013 at 10:06

-1 votes

Interpretation of the Second Incompleteness Theorem

answered Mar 3, 2016 at 21:56

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30 Answers

What axioms are used to prove Gödel's Incompleteness Theorems?

Set theories without "junk" theorems?

Essential reads in the philosophy of mathematics and set theory

Lists as a foundation of mathematics

Dedekind-Peano axioms, but numbers have at most one successor

Is there any formal foundation to ultrafinitism?

Why Does Induction Prove Multiplication is Commutative?

What advantage humans have over computers in mathematics?

Can FPA really prove its consistency?

Relationship between first and second incompleteness theorems

Why Does Induction Prove Multiplication is Commutative?

In what sense does the sentence $\operatorname{con}(\mathsf{PA})$ "say" that $\mathsf{PA}$ is consistent?

How do you restrict the induction axiom in second (or higher) order logic?

Subsystems of Peano arithmetic and incompleteness theorem

Intuitive and/or philosophical explanation for set theory paradoxes

One can earn nothing on the Brownian motion, true ?

Which model of computation is "the best"?

Physics and Church–Turing Thesis

Even XOR Odd Infinities?

Is there any straightforward way to substitute for Gaussian/Brownian assumptions in financial mathematics?

Finite versions of Godel' s incompleteness

History of Logic Development

Can ZFC prove "false theorems", and still be consistent? (was "Junk Theorems" follow up)

Can this weakish system of arithmetic express multiplication for second-sort numbers?

Why is an internal proof of consistency satisfactory for some systems?

The concept of duality

Notable mathematics during World War II

Can FPA really prove its consistency?

Reference request: Minimal Axiomatizations of PA over (+,x,<=).

Interpretation of the Second Incompleteness Theorem