# Questions tagged [lo.logic]

first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.

**209**

**29**answers

### What are some reasonable-sounding statements that are independent of ZFC?

**164**

**15**answers

### Why worry about the axiom of choice?

**164**

**1**answer

### Ultrafilters and automorphisms of the complex field

**141**

**13**answers

### Knuth's intuition that Goldbach might be unprovable

**113**

**10**answers

### Solutions to the Continuum Hypothesis

**110**

**44**answers

### What are the most attractive Turing undecidable problems in mathematics?

**106**

**43**answers

### nontrivial theorems with trivial proofs

**93**

**16**answers

### What if Current Foundations of Mathematics are Inconsistent? [closed]

**93**

**9**answers

### On Mathematical Arguments Against Quantum Computing

**92**

**2**answers

### Does every non-empty set admit a group structure (in ZF)?

**91**

**11**answers

### Checkmate in $\omega$ moves?

**86**

**2**answers

### How would you solve this tantalizing Halmos problem?

**81**

**28**answers

### Sexy vacuity … ${{{{{{}}}}}}$

**79**

**4**answers

### Is the analysis as taught in universities in fact the analysis of definable numbers?

**73**

**7**answers

### How many orders of infinity are there?

**72**

**9**answers

### Is there any formal foundation to ultrafinitism?

**71**

**16**answers

### When are two proofs of the same theorem really different proofs

**70**

**3**answers

### How do I verify the Coq proof of Feit-Thompson?

**68**

**16**answers

### Most 'unintuitive' application of the Axiom of Choice?

**68**

**9**answers

### Can we unify addition and multiplication into one binary operation? To what extent can we find universal binary operations?

**67**

**31**answers

### Can infinity shorten proofs a lot?

**66**

**8**answers

### Succinctly naming big numbers: ZFC versus Busy-Beaver

**63**

**13**answers

### Logic in mathematics and philosophy

**63**

**9**answers

### What's wrong with the surreals?

**63**

**5**answers

### What was Hilbert's view of Gödel's Incompleteness Theorems?

**62**

**4**answers

### Nelson's program to show inconsistency of ZF

**57**

**8**answers

### Set theories without “junk” theorems?

**57**

**9**answers

### Has anyone thought about creating a formal proof wiki with verifier?

**56**

**3**answers

### Forcing as a new chapter of Galois Theory?

**55**

**9**answers

### Arguments against large cardinals

**54**

**19**answers

### What are some results in mathematics that have snappy proofs using model theory?

**54**

**5**answers

### Decidability of chess on an infinite board

**52**

**15**answers

### Abstract Thought vs Calculation

**52**

**2**answers

### Reasons to prefer one large prime over another to approximate characteristic zero

**52**

**3**answers

### What is the geometry of an undecidable diophantine equation?

**51**

**7**answers

### Reductio ad absurdum or the contrapositive?

**51**

**8**answers

### Is all ordinary mathematics contained in high school mathematics?

**51**

**9**answers

### How do they verify a verifier of formalized proofs?

**50**

**14**answers

### What is the high-concept explanation on why real numbers are useful in number theory?

**50**

**8**answers

### What does it mean to suspect that two conjectures are logically equivalent?

**50**

**6**answers

### Has decidability got something to do with primes?

**50**

**5**answers

### The Logic of Buddha: A Formal Approach

**49**

**5**answers

### Is the Riemann Hypothesis equivalent to a $\Pi_1$ sentence?

**49**

**2**answers

### Does Godel's incompleteness theorem admit a converse?

**48**

**10**answers

### What are some important but still unsolved problems in mathematical logic?

**48**

**5**answers

### Does anyone know a polynomial whose lack of roots can't be proved?

**47**

**7**answers

### Is the ultraproduct concept fundamentally category-theoretic?

**46**

**7**answers

### In what respect are univalent foundations “better” than set theory?

**46**

**5**answers

### Can the Riemann hypothesis be undecidable?

**46**

**4**answers