38

Answers

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6

Non-constructive proofs vs. efficient algorithms

2

Computable nonstandard models for weak systems of arithemtic

1

Do all uncountable sets contain elements with infinite Kolmogorov complexity?

0

Is there a general theory of models that has as instances classical FOL, classical propositional logic, etc.?

2

All properties of a mathematical object

3

Oracle Results: P^A = NP^A

0

How small can a language in NP\P be?

2

Solving NP problems in (usually) Polynomial time?

1

Ordinals and complexity classes

1

A programming language that can only create algorithms with polynomial runtime?

2

Is the Axiom of Union independent of the rest of ZF?

2

Formal verification in complexity theory

1

Has Oracles actually provided intuition for proving anything in Complexity Theory?

4

Definition of relativization of complexity class

1

truth vs. provability for ordered fields

6

Proof systems and their hierarchy

3

Propositions equivalent to the completeness of the real numbers

2

Why can Diophantine equations represent exponential growth?

4

Don’t the axioms of set theory implicitly assume numbers?

1

logics restricted in arithmetic hierarchy

2

Difference between turnstile and implication

3

Is there a general setting for self-reference?

2

Derivability conditions for Robinson arithmetic

10

Interpretation of the Second Incompleteness Theorem

10

Where to publish a paper on the Mafia game?

2

Most ‘obvious’ open problems in complexity theory

9

Descriptive complexity theoretic-characterizations of P and NP

1

Succinctly naming big numbers: ZFC versus Busy-Beaver

2

Are computable models sufficient?

2

The best text to study both incompleteness theorems