User Asaf Karagila

160 votes

28 answers

30k views

How to present mathematics to non-mathematicians?

asked Nov 24, 2010 at 9:29

53 votes

1 answer

6k views

Does $2^X=2^Y\Rightarrow |X|=|Y|$ imply the axiom of choice?

asked Nov 17, 2011 at 21:42

53 votes

1 answer

4k views

When does $A^A=2^A$ without the axiom of choice?

asked Feb 24, 2013 at 5:43

50 votes

0 answers

2k views

How many algebraic closures can a field have?

asked Mar 19, 2019 at 9:41

27 votes

1 answer

2k views

How hard is it to destroy a diamond? (with a real)

asked May 26, 2015 at 16:54

27 votes

1 answer

4k views

If $V$ is a vector space with a basis. $W\subseteq V$ has to have a basis too?

asked Nov 12, 2011 at 18:02

26 votes

2 answers

3k views

Sizes of bases of vector spaces without the axiom of choice

asked Apr 5, 2012 at 19:17

24 votes

2 answers

2k views

Short proof of $\frak p=t$

asked May 25, 2014 at 17:33

23 votes

1 answer

4k views

A recommended roadmap into inner models

asked Aug 17, 2011 at 16:25

22 votes

1 answer

2k views

The Continuum Hypothesis and Countable Unions

asked Jan 25, 2012 at 11:45

22 votes

4 answers

3k views

What sort of large cardinal can $\aleph_1$ be without the axiom of choice?

asked Feb 3, 2012 at 13:10

22 votes

3 answers

3k views

Half Cantor-Bernstein without choice

asked May 18, 2011 at 20:57

22 votes

2 answers

2k views

If ZFC has a transitive model, does it have one of arbitrary size?

asked May 5, 2013 at 8:59

22 votes

1 answer

1k views

When will the real numbers be Borel?

asked Jun 10, 2018 at 6:55

20 votes

2 answers

2k views

What is $\omega_1^{CK}(\mathsf{Ord})$?

asked Dec 17, 2012 at 11:31

20 votes

2 answers

3k views

What is a Choice Principle, really?

asked Aug 5, 2012 at 12:30

19 votes

0 answers

905 views

What examples of existence forcing proofs are there?

asked Jun 5, 2019 at 10:28

19 votes

1 answer

815 views

If all reals are generic, is the set of reals generic?

asked Jul 10, 2014 at 8:16

19 votes

6 answers

3k views

Sierpinski's construction of a non-measurable set

asked Dec 22, 2014 at 5:50

18 votes

2 answers

1k views

Haar measures in Solovay's model

asked Jul 17, 2011 at 12:03

18 votes

1 answer

4k views

Countable unions and the axiom of countable choice

asked Sep 7, 2011 at 12:51

18 votes

5 answers

2k views

Forcing over models without the axiom of choice

asked Sep 26, 2011 at 15:37

17 votes

2 answers

3k views

Does ZFC prove the universe is linearly orderable?

asked Oct 27, 2012 at 1:20

17 votes

1 answer

1k views

Is there an $L$ like inner model for $\sf Z$?

asked Oct 25, 2014 at 4:14

17 votes

1 answer

475 views

Is there an infinite set $X$ such that for every isotone $f\colon[X]^\omega\to[X]^\omega$ there is a free decreasing sequence?

asked Dec 6, 2017 at 14:30

15 votes

2 answers

1k views

Brief history of cardinal characteristics of the continuum

asked Dec 14, 2017 at 11:16

15 votes

1 answer

2k views

Hartogs number and the three power sets

asked May 30, 2012 at 11:51

15 votes

1 answer

1k views

Is it consistent relative to ZF that $\frak c = \aleph_\omega$?

asked Oct 19, 2011 at 23:52

14 votes

4 answers

2k views

How elementary can we go?

asked Jul 28, 2011 at 22:50

14 votes

1 answer

2k views

Intuition behind the diagonal intersection

asked Sep 14, 2012 at 13:18

Stack Exchange Network

131 Questions

How to present mathematics to non-mathematicians?

Does $2^X=2^Y\Rightarrow |X|=|Y|$ imply the axiom of choice?

When does $A^A=2^A$ without the axiom of choice?

How many algebraic closures can a field have?

How hard is it to destroy a diamond? (with a real)

If $V$ is a vector space with a basis. $W\subseteq V$ has to have a basis too?

Sizes of bases of vector spaces without the axiom of choice

Short proof of $\frak p=t$

A recommended roadmap into inner models

The Continuum Hypothesis and Countable Unions

What sort of large cardinal can $\aleph_1$ be without the axiom of choice?

Half Cantor-Bernstein without choice

If ZFC has a transitive model, does it have one of arbitrary size?

When will the real numbers be Borel?

What is $\omega_1^{CK}(\mathsf{Ord})$?

What is a Choice Principle, really?

What examples of existence forcing proofs are there?

If all reals are generic, is the set of reals generic?

Sierpinski's construction of a non-measurable set

Haar measures in Solovay's model

Countable unions and the axiom of countable choice

Forcing over models without the axiom of choice

Does ZFC prove the universe is linearly orderable?

Is there an $L$ like inner model for $\sf Z$?

Is there an infinite set $X$ such that for every isotone $f\colon[X]^\omega\to[X]^\omega$ there is a free decreasing sequence?

Brief history of cardinal characteristics of the continuum

Hartogs number and the three power sets

Is it consistent relative to ZF that $\frak c = \aleph_\omega$?

How elementary can we go?

Intuition behind the diagonal intersection