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Results tagged with ho.history-overview
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user 11115
History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.
16
votes
2
answers
1k
views
Von Neumann's consistency proof
In the paper Zur Hilbertschen Beweistheorie, John Von Neumann has proposed a consistency proof for
a fragment of first-order arithmetic (the fragment without induction and with
the successor axioms on …
- 32.2k
7
votes
1
answer
465
views
Historical question about the $\aleph_2$-Souslin hypothesis
For an uncountable regular cardinals $\kappa,$ let $\kappa$-Souslin hypothesis, denoted $SH(\kappa)$ be the assertion that there are no $\kappa$-Souslin trees.
By a result of Jensen, $GCH+SH(\aleph_1) …
- 32.2k
8
votes
0
answers
391
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Silver's unpublished work on reverse Easton iteration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 …
- 32.2k
8
votes
1
answer
534
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 av …
7
votes
0
answers
196
views
$\alpha$-minimal degrees for singular $\alpha$
An important question in $\alpha$-recursion theory is whether there is a minimal $\alpha$-degree at $\alpha=\aleph_\omega.$
Question 1. Who first introduced the above question, and where can I find m …
- 32.2k
9
votes
0
answers
298
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On an unpublished result of Magidor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 $2^{\aleph_\omega}=\aleph_{ …
- 32.2k
12
votes
1
answer
864
views
Higgs paper ``A category approach to Boolean valued set theory''
As Philip Scott says
about Denis Higgs:
In category theory, he wrote an influential and beautiful long paper, "A
category approach to Boolean valued set theory", which initiated many
early students i …
- 32.2k
9
votes
1
answer
411
views
Elements of the method of forcing in some papers of N. N. Luzin
In the paper
Eléments de la méthode de forcing dans quelques travaux de N. N. Lousin. (French) [Elements of the method of forcing in some papers of N. N. Luzin] Amphora, 469–479, Birkhäuser, Basel …
- 32.2k
15
votes
6
answers
2k
views
The origins of forcing in mathematical logic and other branches of mathematics
As everyone knows, forcing was created by Cohen to answer questions in set theory.
Question 1. What are the first applications of set theoretic forcing in other branches of mathematical logic, like n …
18
votes
3
answers
2k
views
Scott-Solovay unpublished paper on ``Boolean valued models of set theory''
I have read some papers from 1970$^{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 resul …
- 32.2k
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 proper …
- 32.2k