# 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.

**29**

**2**answers

### Similarities between Post's Problem and Cohen's Forcing

**164**

**15**answers

### Why worry about the axiom of choice?

**36**

**0**answers

### Concerning the various proofs from the axiom of choice that R^3 admits of surprising geometrical decompositions into circles, skew lines and so on: can we prove in any instance that there are no Borel such decompositions? Or that AC is required?

**15**

**2**answers

### Does ZFC prove the universe is linearly orderable?

**16**

**3**answers

### Pi1-sentence independent of ZF, ZF+Con(ZF), ZF+Con(ZF)+Con(ZF+Con(ZF)), etc.?

**9**

**1**answer

### Reference for Wang Tile

**209**

**29**answers

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

**110**

**44**answers

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

**113**

**10**answers

### Solutions to the Continuum Hypothesis

**79**

**4**answers

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

**92**

**2**answers

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

**55**

**9**answers

### Arguments against large cardinals

**45**

**6**answers

### Is the non-triviality of the algebraic dual of an infinite-dimensional vector space equivalent to the axiom of choice?

**42**

**7**answers

### Why should we believe in the axiom of regularity?

**13**

**0**answers

### Is the universality of the surreal number line a weak global choice principle?

**91**

**11**answers

### Checkmate in $\omega$ moves?

**57**

**8**answers

### Set theories without “junk” theorems?

**49**

**5**answers

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

**54**

**5**answers

### Decidability of chess on an infinite board

**23**

**2**answers

### Large cardinal axioms and Grothendieck universes

**32**

**8**answers

### Arithmetic fixed point theorem

**32**

**6**answers

### A remark of Connes

**24**

**3**answers

### Who needs Replacement anyway?

**26**

**2**answers

### Can there be an embedding j:V to L, from the set-theoretic universe V to the constructible universe L, when V not= L?

**29**

**4**answers

### Is it possible to define higher cardinal arithmetics

**22**

**6**answers

### Where in ordinary math do we need unbounded separation and replacement?

**21**

**1**answer

### Gödel's Constructible Universe in Infinitary Logics (A Possible Approach to HOD Problem)

**13**

**1**answer

### finite dimensional real division algebras

**86**

**2**answers

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

**50**

**14**answers

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

**66**

**8**answers

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

**42**

**2**answers

### A question about ordinal definable real numbers

**18**

**11**answers

### Is PA consistent? do we know it?

**23**

**3**answers

### Is the statement that every field has an algebraic closure known to be equivalent to the ultrafilter lemma?

**18**

**6**answers

### Interesting meta-meta-mathematical theorems?

**30**

**3**answers

### Is there a computable model of ZFC?

**15**

**5**answers

### Hahn-Banach without Choice

**26**

**2**answers

### What is the theory of local rings and local ring homomorphisms?

**23**

**5**answers

### Are the two meanings of “undecidable” related?

**25**

**4**answers

### What is the definition of a large cardinal axiom?

**17**

**3**answers

### Large categories vs. $\mathrm{U}$-categories: why is the loss of category-theoretic information inessential?

**21**

**2**answers

### What is the largest Laver table which has been computed?

**20**

**3**answers

### Cohen reals and strong measure zero sets

**20**

**7**answers

### Does every set admit a rigid binary relation? (and how is this related to the Axiom of Choice?)

**19**

**2**answers

### What is a Choice Principle, really?

**16**

**5**answers

### Morse-Kelley set theory consistency strength

**15**

**3**answers

### On statements independent of ZFC + V=L

**20**

**2**answers

### If ZFC has a transitive model, does it have one of arbitrary size?

**13**

**1**answer

### What metatheory proves $\mathsf{ACA}_0$ conservative over PA?

**13**

**2**answers