# 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.

**5**

**1**answer

### Function on the set of limit countable ordinals

**2**

**1**answer

### Non-existence of countable base of arbitrary ultrafilter

**0**

**2**answers

### Existence of $\alpha$-sequence of infinitesimal sequences with $\alpha>\omega_1$

**-2**

**0**answers

### Cardinals from ordinals in ZFC [on hold]

**0**

**0**answers

### Some questions regarding “Elementary Embeddings and Correctness”

**6**

**0**answers

### Complexity of the set of closed subsets of an analytic set

**7**

**0**answers

### Making the precaliber number bigger than all Knaster numbers

**14**

**1**answer

### Do we know the consistency strength of the Singular Cardinal Hypothesis failing on an uncountable cofinality?

**3**

**1**answer

### K-analytic spaces whose any compact subset is countable

**12**

**1**answer

### End-extending cardinals

**2**

**2**answers

### Who first discovered the concept corresponding to the symbol of class comprehension?

**3**

**1**answer

### Radin forcing preserving large cardinals

**13**

**2**answers

### Set-theoretical foundations of Mathematics with only bounded quantifiers

**2**

**1**answer

### Proving that family of sets has non-empty intersection

**5**

**1**answer

### Number of ultrafilters in an extender

**5**

**1**answer

### Radin generics from iterated ultrapowers

**3**

**0**answers

### A consistent way to “decide” independent statements [closed]

**2**

**0**answers

### Cardinal characteristics of the ideal of $\sigma$-continuity of the Pawlikowski function

**7**

**1**answer

### Cardinal characteristics of amorphous sets

**3**

**0**answers

### Is there a standard meaning for this notation for ordinals in set theory?

**1**

**0**answers

### Two small uncountable cardinals related to Q-sets

**2**

**1**answer

### The trace of the filter on a big subset

**5**

**2**answers

### Ordered union of Borel sets

**-2**

**0**answers

### Can every first order theory have a finitely axiomatizable conservative extension in this sense?

**0**

**0**answers

### Existance of bijective function which maps tensor product of subsets of a selective ultrafilter into the ultrafilter

**21**

**1**answer

### Does “every” first-order theory have a finitely axiomatizable conservative extension?

**7**

**0**answers

### Asymptotically discrete ultrafilters

**10**

**0**answers

### Sunflower / $\Delta$-system lemma in a more general poset?

**5**

**1**answer

### Relation between ultrafilters ${\scr U}$ and ${\scr U} \otimes {\scr U}$ [closed]

**-3**

**0**answers

### Can we get rid of the primitive symbol $V$ in Ackermann's set theory without increment in consistency strength?

**2**

**1**answer

### Dense subfilter of selective ultrafilter

**5**

**1**answer

### Models of $\mathsf{ZFC}$ with neither $P$- nor $Q$-points

**6**

**1**answer

### Finite covers of Boolean algebras by their subalgebras

**-1**

**0**answers

### Largest subset of the powerset of a countable set in which no set includes another [duplicate]

**0**

**0**answers

### Subsets of the unit interval [migrated]

**2**

**2**answers

### (Types of) induction on infinite chains

**5**

**0**answers

### Metrically Ramsey ultrafilters

**5**

**1**answer

### The property of the dense subfilter of a selective ultrafilter

**1**

**1**answer

### Some kind of idempotence of dense filter

**1**

**1**answer

### Semi-rigid boolean algebras

**4**

**0**answers

### Is Ackermann's set theory minus class comprehension equal to ZF?

**5**

**1**answer

### Amorphous proper classes in MK

**40**

**0**answers

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

**15**

**1**answer

### Is Global Choice conservative over Zermelo with Choice?

**0**

**1**answer

### Finitely additive measure on Cartesian square of countable set

**9**

**2**answers

### Examples of transfinite towers

**1**

**1**answer

### Maximal elements in the Rudin-Keisler ordering

**10**

**2**answers

### On the absoluteness of higher Borel sets?

**1**

**0**answers

### Why does $p_{n}(i,1)=1$ so often where the polynomials $p_{n}$ are obtained from the classical Laver tables

**0**

**0**answers