s****f
发帖数: 2 | 1 很多年前学实变的时候,知道了集合的势这个概念,当时有个疑问,自然数集和实数集之
间还有无其他的势,当时没有深究,后来知道这是大问题,哪位大虾能科普一下这个问题
? | b**g
发帖数: 335 | 2 This problem is called "Continuum hypothesis", and is the first problem
in Hilbert's famous list of 21 problems.
The solution is: This hypothesis is neither provable nor disapprovable;
it's independent. (Like the Euclid's parallel postulate in geometry)
Paul Cohen won Fields medal (1966) by constructing an "universe" in which
continuum hypothesis is false.
【在 s****f 的大作中提到】
: 很多年前学实变的时候,知道了集合的势这个概念,当时有个疑问,自然数集和实数集之
: 间还有无其他的势,当时没有深究,后来知道这是大问题,哪位大虾能科普一下这个问题
: ?
| s****f
发帖数: 2 | 3
有点玄,大致能明白
这个"universe"是什么样的,本人只具有一般的本科数学水平,能否通俗的介绍一下?
thank you very much!
【在 b**g 的大作中提到】
: This problem is called "Continuum hypothesis", and is the first problem
: in Hilbert's famous list of 21 problems.
: The solution is: This hypothesis is neither provable nor disapprovable;
: it's independent. (Like the Euclid's parallel postulate in geometry)
: Paul Cohen won Fields medal (1966) by constructing an "universe" in which
: continuum hypothesis is false.
| b**g
发帖数: 335 | 4
which
If you know some algebra, then you should have heard of field extension, i.e.
given a field F, insert something, say, x, to create a new field F[x]
Similarly, begin with a model of axiomatic set theory (e.g. ZFC), say M,
insert
something, say G (G means "generic" set), to it. This G is specially
chosen such that M[G] is still a model of ZFC but violates continuum
hypothesis. (Note: this model M is also special, it has to be countable &
transitive)
This whole process (called "forcing") is
【在 s****f 的大作中提到】
:
: 有点玄,大致能明白
: 这个"universe"是什么样的,本人只具有一般的本科数学水平,能否通俗的介绍一下?
: thank you very much!
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