# 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.

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### Representing $\forall x\in \mathbb{N}$ via ZFC

**5**

**1**answer

### What is the “Prikry–Silver collapse” when CH fails?

**3**

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### A family of finite subsets of an infinite cardinal that is closed enough

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### Can we put a ZFC world inside an NF world?

**6**

**1**answer

### Models with fixed cardinality of non-Lebesgue measurable sets

**5**

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### Induced subgraphs of the almost-disjointness graph

**1**

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### Is this theory using defined notions of classes, sets, and membership interpretable in ZFC?

**10**

**1**answer

### Elementary embeddings and replacement

**5**

**1**answer

### How similar are the c.e. degrees and the CEA(Cohen) degrees?

**16**

**1**answer

### Partitions of the real line into Borel subsets

**6**

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### Better scales and Failures of SCH

**5**

**1**answer

### Dependent choices (DC) in ${\bf HOD}(\mathbb{R},X)$, where $X$ is a set of reals

**5**

**2**answers

### Extending contents

**4**

**1**answer

### Coloring almost-disjointness

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### What is the exact consistency strength of this type-set theory?

**6**

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### Are initial segments of coherent measure sequences coherent?

**2**

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### Banach–Mazur game and mappings

**1**

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### Why $\beta S$ is not a semigroup when $S$ is a (directed) partial semigroup?

**4**

**1**answer

### How to compare three supremums of ordinals eventually writable by Ordinal Turing Machines?

**5**

**2**answers

### Self-homeomorphism of Stone-Čech boundary with an isolated fixed point

**2**

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### Can we have $\sf V=HTD$? How it relates to $\sf V=HOD$?

**0**

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### I have 2 very stupid questions about elements and subsets in ZFC [migrated]

**3**

**2**answers

### Can Z + Ranks + Successor cardinals + Ordinal inaccessibility be equal to ZF?

**3**

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### On a connectivity property of set systems

**14**

**2**answers

### How many category structures are possible on two sets?

**7**

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### How much is known about the consistency strength of toposes and topos-like categories?

**3**

**1**answer

### “Good limit” of an uncountable sequence of elements of an ultrafilter

**0**

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### Dense refinement of $\omega$-cover

**1**

**1**answer

### What does the Concordant constructible universe model?

**11**

**1**answer

### “Drinking number” of a graph

**10**

**2**answers

### How far to find a well-order?

**0**

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### Can all unions of sets above some level be constructible before the sets in some relative constructible universe?

**4**

**1**answer

### Coloring the uncountable Lebesgue-measurable sets of $\mathbb{R}$

**9**

**1**answer

### Do saturated models require choice?

**8**

**0**answers

### Ring of global sections of a functor $\mathbf{CRing} \to \mathbf{Set}$

**0**

**1**answer

### Can we choose a sequence of Hilbert spaces?

**11**

**1**answer

### Does every countable set of Turing degrees have an upper bound, without AC?

**1**

**1**answer

### Is existence of this set consistent with Zermelo set theory minus choice?

**11**

**2**answers

### How many finitely-generated-by-elements-of-finite-order-groups are there?

**12**

**0**answers

### An internal notion of freeness for complete Boolean algebras

**2**

**0**answers

### Can we have a “very strong” cone phenomenon in the Turing degrees (and a related question)?

**1**

**1**answer

### Scales and concentration

**4**

**2**answers

### How large is the supremum of halting times of Infinite Time Turing Machines, assuming that halting times are bounded and inputs are arbitrary?

**0**

**1**answer

### Is a function needed here?

**12**

**1**answer

### Descriptive set theory for computer scientists?

**2**

**0**answers

### Showing that the procedure to generate an algebra does not generate a $\sigma$-algebra

**0**

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### Can this theory that internalize sets from external functions be consistent?

**6**

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### “Relative plausibility” of some infinitary theories

**3**

**1**answer

### Candidate “AEC-yielding” fragments of bad logics

**11**

**1**answer