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abo
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13 votes

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

11 votes

Set theories without "junk" theorems?

11 votes

Lists as a foundation of mathematics

10 votes

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

9 votes

Essential reads in the philosophy of mathematics and set theory

6 votes

Is there any formal foundation to ultrafinitism?

6 votes
Accepted

Why Does Induction Prove Multiplication is Commutative?

6 votes

What advantage humans have over computers in mathematics?

5 votes

Can FPA really prove its consistency?

5 votes
Accepted

Relationship between first and second incompleteness theorems

5 votes

Why Does Induction Prove Multiplication is Commutative?

3 votes

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

3 votes

Subsystems of Peano arithmetic and incompleteness theorem

2 votes
Accepted

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

2 votes

Intuitive and/or philosophical explanation for set theory paradoxes

2 votes

One can earn nothing on the Brownian motion, true ?

2 votes

Which model of computation is "the best"?

2 votes

Physics and Church–Turing Thesis

1 vote

Even XOR Odd Infinities?

1 vote

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

1 vote

Finite versions of Godel' s incompleteness

1 vote

History of Logic Development

1 vote

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

1 vote

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

1 vote

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

1 vote

The concept of duality

1 vote

Notable mathematics during World War II

0 votes

Can FPA really prove its consistency?

0 votes

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

-1 votes

Interpretation of the Second Incompleteness Theorem