**5**

votes

**1**answer

844 views

### Uncountable nonstandard models of PA

Standard techniques (no pun intended) can be used to show that countable nonstandard models of Peano Arithmetic are order isomorphic to $\mathbb{N} + \mathbb{Z} \cdot \mathbb{Q}$. Once we have used ...

**1**

vote

**1**answer

598 views

### Metrization of hyperreals

Hello,
i was reading your article about non metrizability of *R.
i was able to prove that the interval open topology is not metrizable by proving that the intersection of decreasing hyper-intervals ...

**7**

votes

**9**answers

3k views

### Would Euler's proofs get published in a modern math Journal, especially considering his treatment of the Infinite?

I was wondering how mathematicians of today would treat, for example, Euler's proof of zeta(2).
In William Dunham's book 'Journey through Genius' ( ...

**12**

votes

**9**answers

3k views

### nonstandard analysis book recommendation

I wish to learn nonstandard analysis. Are there any good book recommendations? I'm familiar with the ZFC system, and learnt analysis the classical way. I've found some undergraduate texts, but they ...

**38**

votes

**16**answers

6k views

### How helpful is non-standard analysis?

So, I can understand how non-standard analysis is better than standard analysis in that some proofs become simplified, and infinitesimals are somehow more intuitive to grasp than epsilon-delta ...

**34**

votes

**4**answers

3k views

### Which topological spaces admit a nonstandard metric?

My question is about the concept of nonstandard metric space that would arise from a use of the nonstandard reals R* in place of the usual R-valued metric.
That is, let us define that a topological ...

**18**

votes

**5**answers

1k views

### Isomorphism types or structure theory for nonstandard analysis

My question is about nonstandard analysis, and the diverse possibilities for the choice of the nonstandard model R*. Although one hears talk of the nonstandard reals R*, there are of course many ...