# 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.

**0**

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### On a particular proof of “if the sharp of every real exists and every club contains a club constructible from a real, then $\delta^1_2 = \omega_2$”

**2**

**1**answer

### Constructing a section of an equivalence relation compatible with the intersection

**-2**

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### Wadge hierarchy on $\Delta^0_2$ sets [closed]

**5**

**0**answers

### Are there analogues of real-valued measurability for larger powersets?

**16**

**0**answers

### Čech functions and the axiom of choice

**3**

**1**answer

### NF and incompleteness

**-3**

**0**answers

### Ackermann function is computable [closed]

**43**

**4**answers

### Category theory and set theory: just a different language, or different foundation of mathematics?

**6**

**1**answer

### Can we recover an inner model of CH after forgetting some generic information?

**12**

**1**answer

### How strong a set theory is necessary for practical purposes in sheaf theory?

**15**

**0**answers

### Positive set theory and the “co-Russell” set

**3**

**0**answers

### Maximum partite subset of edges of a hypergraph

**0**

**0**answers

### At which large cardinal property Ackermann set theory + finitization rule would stop?

**0**

**0**answers

### Is Separation in $V$ a theorem schema of Ackermann set theory minus subsets?

**4**

**0**answers

### Does $\mathbb{R}$ have a partite subbase?

**2**

**1**answer

### Centralizer of a single element in the monoid of self-maps of a set

**4**

**1**answer

### Implications of the existence of a pair of surjective functions, without Axiom of Choice

**0**

**0**answers

### Is there a formula with one free variable in NBG that defines a class that does not exist?

**2**

**1**answer

### Atomless, c-additive measures in ZFC

**3**

**1**answer

### Finitely additive, $\kappa$-additive atomless measures in ZFC

**11**

**0**answers

### Isomorphic free groups have bijective generating sets

**5**

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### For which classes of metric spaces can we prove that quasi-isometry is an equivalence relation in ZF?

**10**

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### How wealthy are canonical inner models?

**23**

**1**answer

### Are Conway's combinatorial games the “monster model” of any familiar theory?

**5**

**1**answer

### Preserve unbounded sets between different cofinality

**13**

**3**answers

### Tarski's truth theorem — semantic or syntactic?

**1**

**2**answers

### Connected Hausdorff spaces with large collection of disjoint open sets

**16**

**1**answer

### Has the exponentiation of ordinals a nice geometric model?

**7**

**1**answer

### Is Axiom of Choice equivalent to its version for families of sets, indexed by ordinals? [duplicate]

**8**

**1**answer

### On the utility of Silver machines

**11**

**2**answers

### For what sets $X$ do there exist a pair of functions from $X$ to $X$ with the identity being the only function that commutes with both?

**28**

**2**answers

### Who introduced direct limits?

**6**

**1**answer

### Complexity of a combinatorial constraint

**6**

**1**answer

### Regular limit points of possible cofinalities

**5**

**0**answers

### Selecting an almost disjoint family in a given family of sets

**2**

**1**answer

### Collection of pairwise non-isomorphic infinite self-complementary graphs

**2**

**1**answer

### What is the smallest cardinality of a base of an ultrafilter on $\omega$ related to an almost disjoint family of cardinality $\mathfrak c$?

**4**

**1**answer

### What is the smallest cardinality of a maximal ultrafamily of infinite subsets of $\omega$?

**54**

**4**answers

### Bourbaki's definition of the number 1

**2**

**0**answers

### ITTMs with higher types

**13**

**1**answer

### History of well founded relations

**2**

**2**answers

### In the von Neumann–Bernays–Gödel axiomatic system, the Axiom of Transposition can be simplified

**1**

**2**answers

### Covering dimension of uncountable union of compact spaces

**4**

**1**answer

### Function whose graph is a Borel relation

**7**

**0**answers

### “Local” compactness properties beyond $\mathcal{L}_{\omega_1,\omega}$?

**0**

**0**answers

### Can inaccessibility be captured in relational flat set theory?

**3**

**0**answers

### Global choice for models of complete theories in $\mathsf{ZFC}$

**1**

**1**answer

### Borel hierarchy and tail sets

**0**

**1**answer

### Lambda system generated by a non-atomic collection

**5**

**0**answers