All Questions
Tagged with forcing nt.number-theory
7 questions
12
votes
2
answers
1k
views
Am I doing a forcing argument here?
I have an argument of the following form:
Executive Summary:
We have a $\mathbb R$-valued function $L$ which we want to show is $\mathbb Z$-valued. We approximate it by $\mathbb Q$-valued functions $\...
- 63.9k
5
votes
0
answers
536
views
A set theoretic approach to the Riemann hypothesis
Let $X$ be an extremally disconnected
(i.e. such that the closure of open sets is open) compact Hausdorff space. Then
$*_1$ $C(X)$
is the space of continuous functions $f: X \to \mathbb{C}$,
$*_2$ $C^...
- 32.1k
82
votes
3
answers
20k
views
Czelakowski's claimed proof of the Twin Prime Conjecture
It seems like the article "The Twin Primes Conjecture is True in the Standard Model of Peano Arithmetic: Applications of Rasiowa–Sikorski Lemma in Arithmetic (I)" by Janusz Czelakowski ...
- 1,083
8
votes
2
answers
752
views
Paul Cohen on genesis of method of forcing and mathematical similarities
We have on record Paul Cohen's comments on being inspired by issues of formalizing algorithms in number theory (this needs to be verified as per comment) as well as related remarks on computability. ...
- 16.6k
8
votes
1
answer
393
views
Largeness and arithmetic progression properties of generic reals
Consider the following properties for a subset $A$ of $\mathbb{N}$:
(1) $A$ is large: $\sum_{n \in A}$$ 1\over n$$=\infty,$
(2) $A^\infty=\limsup \frac{|A \cap \{ 1, \dots, n\}|}{n} >0$,
(3) $A_\...
- 32.1k
6
votes
1
answer
535
views
Adding sets not containing arithmetic progressions of length three by forcing
Consider the following forcing notion: conditions in $\mathbb{P}$ are pairs $(s, N),$ where:
1) $s\in 2^{<\omega}$,
2) $N\in \mathbb{N}$,
3) (by identifying $s$ with a subset of $lh(s)$) $s$ ...
- 32.1k
4
votes
4
answers
3k
views
Where do Set Theory and Number Theory meet together?
As all know, by absoluteness theorems in Set Theory, most of theorems in number theory are $ZFC$-provable if and only if they are consistent with $ZFC$, it's because of absoluteness of essence of ...
- 2,381