In article <5n1up2$o4r$1@news.fas.harvard.edu>, kubo@noether (Tal Kubo) writes: >Matthew P Wiener <weemba@sagi.wistar.upenn.edu> wrote:
>>>[lack of finite models to formulate 0-1 laws with]
>>You have already reached agreement that some sort of finite finesse >>could be "fudged".
>That's stretching it. I said I'm willing to believe it could >potentially be solved, and pointed to more immediate problems. I've >definitely not "reached agreement" that it's a non-issue.
I didn't claim it's not a non-issue either. Just that even you seem to think it's not a particularly reaching idea.
>>Everything has countable models, so I want the theory of >>the first k members, for k very large.
>What does that mean, for PA say? How do probabilities or the like >come into the picture?
Take PA, and bound all the quantifiers in the axioms with various growth functions.
>>> Not that 0-1 >>>laws, when present, ever produce fewer than uncountably many >>>different models, let alone a SINGLE one as you claim.
>>0-1 laws only produce uncountably many different models, by the way, >>when you have no further information.
>What extra-information exemption are you talking about?
The Goedelian situation, in this case.
> Do you >have an example involving a known 0-1 law?
That's utterly trivial. Select a single model, and describe it in a more detailed second order manner. For example, graphs can be thought of as defined on integers, so just give it explicitly.
>> That is not the case here.
>It's hard to determine what is the case here, since we have >only the most nebulous statements to go on.
The above extra-information exemption is only quite explicit. -- -Matthew P Wiener (weemba@sagi.wistar.upenn.edu)
