# 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.

**6**

**3**answers

### How do we formally construct the successor universe $\mathscr{U}^+$ of a universe $\mathscr{U}$ in $\mathsf{ZFC}$?

**12**

**1**answer

### Translating Grothendieck axiom UB into ZFC

**0**

**0**answers

### Can MK be interpreted in a class theory about an abstract hierarchy principle + an accessibility principle?

**6**

**1**answer

### Action of infinite symmetric groups on iterated power sets

**1**

**1**answer

### Enumeration Hierarchies

**9**

**0**answers

### What happens when you iterate Cohen reals?

**10**

**1**answer

### Looking for “Set theory for a small universe” by Ketonen

**10**

**0**answers

### stationary reflection in $[\kappa]^\omega$

**6**

**0**answers

### Singular strong generator

**1**

**1**answer

### A proof of recontruction of Sacks generic filter from it's Sacks real (M[G] = M[f])

**11**

**1**answer

### The Parovichenko cardinal, is it equal to $\max\{\aleph_2,\mathfrak p\}$?

**3**

**1**answer

### Function $f:\kappa\to\alpha$ with small fibers where $\alpha\in\kappa$

**14**

**0**answers

### O-minimality and forcing

**0**

**2**answers

### Are Regularity schema and $\in$-induction schema equivalent in intuitionistic logic?

**23**

**0**answers

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

**7**

**1**answer

### A ridiculous combinatorial cardinal characteristic of the continuum?

**7**

**3**answers

### Characterizing “bounded” distributivity in terms of dense open sets

**4**

**1**answer

### bijections and order types

**1**

**2**answers

### Does Regularity schema imply $\in$-induction when added to first order Zermelo set theory?

**-1**

**1**answer

### Injective choice function for non-separable $T_2$-spaces

**0**

**1**answer

### Support of a regular measure Reg

**2**

**1**answer

### Is $\in$-induction provable in first order Zermelo set theory?

**4**

**0**answers

### Ordinal analysis and nonrecursive ordinals

**7**

**1**answer

### Can a Shelah semigroup be commutative?

**11**

**1**answer

### Completeness number of ultrafilters

**5**

**1**answer

### $\Delta^{1}_{2}$ and degrees of constructibility $\textbf{on sets}$

**6**

**0**answers

### On the number $n_0$ in Shelah's construction of a Jonsson group

**3**

**0**answers

### On Khelif's example of a group of countable cofinality having the Bergman property

**12**

**1**answer

### A Shelah group in ZFC?

**3**

**0**answers

### Completely I-non-measurable unions in Polish spaces

**10**

**1**answer

### Relation between the Axiom of Choice and a the existence of a hyperplane not containing a vector

**0**

**0**answers

### Is there a known shorter axiomatization of NF than this?

**2**

**1**answer

### A possible characterization of regular cardinals?

**4**

**2**answers

### The cofinality of the poset $[\kappa]^{<\kappa}$ for a singular cardinal $\kappa$

**9**

**0**answers

### A ZFC-example of a countably compact paratopological group which is not a topological group

**8**

**1**answer

### A combinatorial property of uncountable groups, II

**6**

**1**answer

### A combinatorial property of uncountable groups

**7**

**1**answer

### Enhancing Grothendieck's universes and Grothendieck's axiom: Feferman's universe

**11**

**3**answers

### Cardinality of families of subsets of $\mathbb{N}$ whose intersections are finite

**7**

**1**answer

### Can $\Delta^{1}_{2}$ separate degrees of constructibility?

**3**

**0**answers

### If any satisfiable $\mathcal{L}_{κ,κ}(Q_{=κ})$-theory remains satisfiable when replacing $Q_{=κ}$ with $Q_{=μ}$, is $κ$ huge?

**7**

**1**answer

### Can we inductively define Wadge-well-foundedness?

**2**

**0**answers

### C.c.-ness of a forcing notion based on an atomless complete Boolean algebra

**0**

**1**answer

### What are the difficulties involved in proving that the Kunen inconsistency holds in $NGB$

**5**

**2**answers

### Is there a set $S\subseteq [0,1]$ with $|S|=2^{\aleph_0}$ and distinct pairwise distances?

**9**

**3**answers

### A property of an ultrafilter

**4**

**1**answer

### Generalizing the $T_0$-axiom

**3**

**1**answer

### $|V|$ and $|E|$ in hypergraphs with a separation property

**4**

**1**answer

### Hereditarily indecomposable groups

**2**

**1**answer