# Questions tagged [set-theory]

forcing, large cardinals, descriptive set theory, infinite combinatorics, cardinal characteristics, forcing axioms, ultrapowers, measures, reflection, pcf theory, models of set theory, axioms of set theory, independence, axiom of choice, continuum hypothesis, determinacy, Borel equivalence relations, Boolean-valued models, embeddings, orders, relations, transfinite recursion, set theory as a foundation of mathematics, the philosophy of set theory.

**44**

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### Set-theoretic reformulation of the invariant subspace problem

**40**

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### How many algebraic closures can a field have?

**36**

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### 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?

**28**

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### Where do uncountable models collapse to?

**25**

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### Can one divide by the cardinal of an amorphous set?

**25**

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### Supercompact and Reinhardt cardinals without choice

**23**

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### Is it still an open problem whether $\mathbb{R}^\omega$ is normal in the box topology?

**22**

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### CH and automorphisms of ultrapowers of $\mathbb{Z}$ and $\mathbb{R}$

**21**

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### Relative null-ness

**21**

**0**answers

### categorical characterization of large cardinals

**21**

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### Subfields of $\mathbb{C}$ isomorphic to $\mathbb{R}$ that have Baire property, without Choice

**20**

**0**answers

### A question about small sets of reals

**18**

**0**answers

### Is this Variation of the Continuum Hypothesis Inconsistent with ZFC or ZF?

**18**

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### The cofinality of $(\mathbb{N}^\kappa,\le)$ for uncountable $\kappa$?

**18**

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### Souslin trees on the first inaccessible cardinal

**18**

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### Antichains of Cardinals in ZF Without Choice…

**17**

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### Is it consistent with ZF that $V\to V^{\ast \ast}$ is always surjective?

**17**

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### Does the pointclass of universally Baire sets always have the uniformization property?

**17**

**0**answers

### Hahn-Banach and the “Axiom of Probabilistic Choice”

**17**

**0**answers

### Souslin trees and weakly compact cardinals

**17**

**0**answers

### Are there lightweight foundations for arbitrarily extendable objects?

**16**

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### Does every real function have this weak derivation property?

**16**

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### Gitik's work on Shelah's weak hypothesis

**16**

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### Ramsey's theorem for the first uncountable ordinal

**16**

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### Gap two Sierpinski set?

**16**

**0**answers

### Do all countable $\omega$-standard models of ZF with an amorphous set have the same inclusion relation up to isomorphism?

**16**

**0**answers

### Ideas behind Gitik's solution of PCF conjecture

**15**

**0**answers

### A question about sigma algebras and rectangles

**15**

**0**answers

### The axiom $I_0$ in the absence of $AC$

**15**

**0**answers

### To what extent does (co)homology of groups made discrete depend on set theory?

**14**

**0**answers

### Does inner model theory seek canonical models for large cardinals?

**14**

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### O-minimality and forcing

**14**

**0**answers

### Cardinality vs. isomorphism type of vector spaces without choice

**14**

**0**answers

### Cohen/Random reals over intermediate models in countable support iterations

**14**

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### The failure of GCH al $\aleph_\omega$ by nice forcing

**14**

**0**answers

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

**14**

**0**answers

### A meager subgroup of the real line, which cannot be covered by countably many closed subsets of measure zero?

**14**

**0**answers

### Adding a saturated ideal

**14**

**0**answers

### Is $\mathbb{Z}^{\omega}$ ever the union of a chain of proper subgroups each isomorphic to $\mathbb{Z}^{\omega}$?

**14**

**0**answers

### Are there additive subgroups of reals of dimension 1 with no subgroups of dimension strictly between 0 and 1?

**13**

**0**answers

### Consistency strength of $j:L_δ→L_δ$ for some δ

**13**

**0**answers

### Covering S2 with great circles

**13**

**0**answers

### Small cardinals related to topological convergence

**13**

**0**answers

### If $U,D$ are $\kappa$-complete nonprincipal ultrafilters on $\kappa$ and $j_U(U) = j_D(D)$, is $U=D$?

**13**

**0**answers

### Arguments against Freiling's argument against Continuum Hypothesis

**13**

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### Non meager union of lines

**13**

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### How much choice is required to prove concretizability theorems in category theory?

**13**

**0**answers

### How to measure the strength of Zermelo over bounded Zermelo?

**12**

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### L-spaces without convergent sequences

**12**

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