6
votes
2answers
450 views

Survey of the history of calculus?

Boyer 1939 is a nice readable survey of the history of the calculus, but it's showing its age. Discussing the notion of instantaneous velocity, he has: Mathematics knows no minimum interval of ...
2
votes
0answers
353 views

Deducing Skolem's nonstandard integers from downward Lowenheim-Skolem?

If one has a nonstandard model $\mathcal{N}$ of PA and adjoins to the first-order theory the countable list of axioms $1<H,\, 2<H,\, 3<H, \ldots$ (satisfied in $\mathcal{N}$) for all the ...
9
votes
4answers
490 views

dense orders are saturated

In a FOM msg of Fri May 21 19:59:44 EDT 1999, http://www.cs.nyu.edu/pipermail/fom/1999-May/003149.html Simpson gave a short proof of the following theorem: Theorem. Let F be a real closed ordered ...
16
votes
2answers
1k views

Non standard Algebraic Topology

Let *$\mathbb R$ a field of non-standard real numbers (or any real closed field) equipped with its natural generalized metric $d(x,y)=|x-y|$. Equip *$\mathbb R^2$ and *$\mathbb R^3$ with the ...