# 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.

**9**

**1**answer

### A question on the ultrafilter number

**2**

**0**answers

### Covering numbers - looking for a more combinatorial proof

**7**

**1**answer

### Non-tensor-representable ultrafilters on $\omega$

**7**

**1**answer

### Is there an abstract theory of club sets and stationary sets?

**3**

**1**answer

### Minimal cardinality of a filter base of a non-principal uniform ultrafilters

**1**

**0**answers

### Growth rate of the critical points of the Fibonacci terms $t_{n}(x,y)$ vs $t_{n}(1,1)$ in the classical Laver tables

**1**

**0**answers

### Attraction in Laver tables

**8**

**1**answer

### Axiom of choice and algebraic tensor product

**5**

**1**answer

### Amalgamation via elementary embeddings

**1**

**0**answers

### Multiple roots in the classical Laver tables

**4**

**0**answers

### Universal and strong $Q$-sets

**4**

**1**answer

### Is this lemma equivalent to the axiom of choice?

**1**

**1**answer

### Maximizing “happy” vertices in splitting an infinite graph

**4**

**1**answer

### The example of the idempotent filter or subsets family with finite intersections property

**1**

**0**answers

### Can we have $\sup\{\alpha\mid(x*x)^{\sharp}(\alpha)>x^{\sharp}(\alpha)\}=\infty$ in an algebra resembling the algebras of elementary embeddings?

**1**

**0**answers

### In the classical Laver tables, do we have $o_{n}(1)<o_{n}(2)$ for any $n>8$?

**3**

**1**answer

### Nonexistence of a 'product universal' compact Hausdorff pseudotopological space?

**2**

**0**answers

### What possible order type can the critical points of these algebras with one generator achieve?

**9**

**2**answers

### Small uncountable cardinals related to $\sigma$-continuity

**5**

**1**answer

### Which branches of mathematics can be done just in terms of morphisms and composition?

**7**

**1**answer

### On infinite combinatorics of ultrafilters

**2**

**0**answers

### For each $n$ is it possible to have $\mathrm{crit}(x^{[n]}*y)>\mathrm{crit}(x^{[n-1]}*y)>\dots>\mathrm{crit}(x*y)$?

**1**

**0**answers

### Vastness of inverse systems of Laver-like algebras

**1**

**0**answers

### Can we always extend a finitely generated reduced Laver-like algebra to a vast inverse system of Laver-like algebras?

**16**

**2**answers

### Raising the index of accessibility

**-4**

**2**answers

### Is the notion of measurable cardinal definable from the perspective of set-theoretical potentialism?

**10**

**1**answer

### Selective ultrafilter and bijective mapping

**4**

**1**answer

### Surreal numbers and the Axiom of Choice

**1**

**0**answers

### Generalization of the linear extension theorem to directed acyclic graphs

**6**

**1**answer

### Locally presentable categories, universes, and Vopenka's principle

**3**

**0**answers

### Ordering large cardinal axioms around the level of $n$-huge by consistency strength?

**2**

**0**answers

### Calibrating the strength of the quotients of subalgebras of the classical Laver tables

**2**

**2**answers

### Are there $2^{\aleph_0}$ pairwise non-isomorphic Boolean algebras on $\omega$?

**5**

**1**answer

### Existence of a strange function

**0**

**0**answers

### Are these conditions sufficient for a self-distributive algebra to occur in the algebras of elementary embeddings?

**5**

**1**answer

### Is it consistent that $|[\kappa]^{<\kappa}| > \kappa$?

**7**

**1**answer

### Explaining the consistency of PRA and ZF from predicative foundations

**0**

**1**answer

### Linear intersection number and chromatic number for infinite graphs

**1**

**0**answers

### Density of different types of critical points in an algebra of elementary embeddings

**1**

**0**answers

### Density of critical points subalgebras of the algebras of elementary embeddings

**6**

**0**answers

### Can one use forcing as a step to prove the Keisler-Shelah isomorphism theorem?

**9**

**0**answers

### Does there exist a non-trivial elementary embedding from an ultrapower $V^{I}/U$ to $V^{I}/U$?

**6**

**1**answer

### Do any finite predictions of Quantum Mechanics depend on the set theoretic axioms used?

**3**

**0**answers

### Partial well-ordering of formulas

**1**

**0**answers

### Is every critically subsimple Laver-like algebra a quotient of a critically simple Laver-like algebra on the same number of generators?

**13**

**1**answer

### What are some good lower bounds on the consistency of the failure of the PCF conjecture?

**4**

**0**answers

### Symmetry between V and HOD

**3**

**0**answers

### Why do highly composite rows on the bad Laver tables have longer periods?

**3**

**1**answer

### Does every directed graph have a directed coloring with $4$ colors?

**6**

**0**answers