[FOM] More Friedman/Baez

[Harvey Friedman]

By the way, in Friedman/Baez  I wrote

"A nonstandard integer is not anything at all, but a point in a model
of PA that is of order type omega. There is only one model of PA of
order type omega up to isomorphism."

which has a very bad typo, which I corrected on those other internet
sites. A nonstandard integer is not anything at all, but a point in a
model of PA that has infinitely many predecessors.

**********************

On Fri, Apr 8, 2016 at 1:28 AM, Lawrence Paulson <lp15 at cam.ac.uk> wrote:
> I learned some axiomatic set theory from AS Kechris at Caltech. I'm pretty sure I remember him describing V=L as "clearly false", the continuum hypothesis likewise. My impression is that he regarded V as some sort of objective reality. Meanwhile, somewhere in Ken Kunen's Set Theory we find a reference to "the real world of cows and pigs".
>
> --lcp
>
Wow! I keep finding people who have a somewhat serious to serious
background in math logic, and migrated, for better or worse, to
adjacent subjects! John Baez is another.

Even among the objective reality people, "CH is clearly false" has
changed quite a bit. Also, as I said and also on other sites, there
has been some serious defectors of this positions, who used to hold it
very strongly. I don't know what Kechris' current views are, but for a
very long time he has focused entirely on descriptive set theory,
which is immune to statements like CH.

On the other hand, the universal hatred of V = L is still around,
because although it completely solves practically all natural set
theoretic problems, at least those anywhere near the reals and sets of
reals, it eliminates a lot of beloved set theory, especially
measurable cardinals and the like.

Of course, even V = L does not touch concrete mathematical statements,
as you well know.

Harvey Friedman