# 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

### Injection into a proper class and choice without regularity

**5**

**1**answer

### Function on the set of limit countable ordinals

**-3**

**0**answers

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

**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]

**11**

**2**answers

### What is the consistency strength of weak Vopenka's principle?

**21**

**4**answers

### What would be some major consequences of the inconsistency of ZFC?

**6**

**0**answers

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

**3**

**1**answer

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

**14**

**0**answers

### Adding a saturated ideal

**7**

**0**answers

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

**5**

**1**answer

### Intersection of iterated powerset in NFU

**2**

**2**answers

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

**12**

**1**answer

### End-extending cardinals

**14**

**1**answer

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

**45**

**4**answers

### The origin of sets?

**216**

**31**answers

### What are some reasonable-sounding statements that are independent of ZFC?

**-3**

**0**answers

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

**61**

**12**answers

### What practical applications does set theory have?

**3**

**1**answer

### Radin forcing preserving large cardinals

**9**

**2**answers

### Terminology about trees

**46**

**8**answers

### Why should we believe in the axiom of regularity?

**13**

**2**answers

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

**3**

**0**answers

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

**117**

**11**answers

### Solutions to the Continuum Hypothesis

**-2**

**0**answers

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

**9**

**4**answers

### Very Large Cardinal Axioms and Continuum Hypothesis

**70**

**19**answers

### Injectivity implies surjectivity

**5**

**1**answer

### Radin generics from iterated ultrapowers

**75**

**20**answers

### Proofs of the uncountability of the reals.

**7**

**3**answers

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

**2**

**1**answer

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

**5**

**1**answer

### Number of ultrafilters in an extender

**8**

**1**answer

### Stationarity and Fodor's lemma for a (nice) poset?

**0**

**3**answers

### Sets = structured sets without structure

**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

**9**

**2**answers

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

**7**

**1**answer

### Cardinal characteristics of amorphous sets

**1**

**1**answer

### Some kind of idempotence of dense filter

**0**

**0**answers

### How slowly can it takes for the Fibonacci terms in a partially permutative self-distributive algebra to stabilize?

**1**

**0**answers

### Is the variety of ternary self-distributive algebras generated by its finite members?

**2**

**1**answer

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

**21**

**1**answer

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

**1**

**0**answers

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

**5**

**2**answers

### Ordered union of Borel sets

**14**

**0**answers

### A meager subgroup of the real line, which cannot be covered by countably many closed subsets of measure zero?

**0**

**0**answers

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

**10**

**0**answers