All Questions
11 questions
49
votes
1
answer
2k
views
Producing finite objects by forcing!
It is a trivial fact that forcing can not produce finite sets of ground model objects. However there are situations,
where we can use forcing to prove the existence of finite objects with some ...
- 32.1k
32
votes
2
answers
4k
views
Similarities between Post's Problem and Cohen's Forcing
Remark: I have since learned that G.H. Moore addresses this question in the third reference listed at the end of this post, beginning on p. 157 in which he cites a letter from Kreisel to Gödel dated 4/...
- 7,831
18
votes
3
answers
2k
views
Scott-Solovay unpublished paper on ``Boolean valued models of set theory''
I have read some papers from 1970$^{th}$, and in some of them, the paper of Scott and Solovay on ``Boolean valued models of set theory'' is given as a main reference, with many references to the ...
- 32.1k
15
votes
6
answers
2k
views
The origins of forcing in mathematical logic and other branches of mathematics
As everyone knows, forcing was created by Cohen to answer questions in set theory.
Question 1. What are the first applications of set theoretic forcing in other branches of mathematical logic, like ...
12
votes
2
answers
1k
views
Origin of the term "generic" in set theory
In set theory, in particular the context of forcing, if $M$ is a model of $\sf ZFC$ and $P\in M$ is a partial order, we say that $G\subseteq P$ is a generic filter (or $M$-generic or generic over $M$) ...
- 39.7k
9
votes
1
answer
414
views
Elements of the method of forcing in some papers of N. N. Luzin
In the paper
Eléments de la méthode de forcing dans quelques travaux de N. N. Lousin. (French) [Elements of the method of forcing in some papers of N. N. Luzin] Amphora, 469–479, Birkhäuser, Basel, ...
- 32.1k
9
votes
0
answers
299
views
On an unpublished result of Magidor
In 1970th, Magidor proved the following important results:
(1) Assuming the existence of a supercompact cardinal, it is consistent that $\aleph_\omega$
is strong limit and $2^{\aleph_\omega}=\aleph_{\...
- 32.1k
9
votes
0
answers
257
views
History of preservation theorems in forcing theory
For my honours thesis, I am studying a general preservation theorem using a framework provided by Shelah. I am mainly concerned about revised countable support iteration of $\dot{S}$-semiproper ...
- 1,328
8
votes
1
answer
535
views
Different approaches to forcing
There are many different approaches to the forcing method, and I am looking for all known such approaches. So my question is:
Question 1. Which different approaches to set theoretic forcing are ...
8
votes
0
answers
394
views
Silver's unpublished work on reverse Easton iteration
Silver was the first person who used the method of reverse Easton iterations in connection with large cardinals, and used it to force the failure of $GCH$ at some measurable cardinal.
At most papers ...
- 32.1k
6
votes
4
answers
2k
views
The history of Proper Forcing
What were the initial motivations of the use of the proper forcing.?