Re: question about categoricity

Torkel Franzen wrote:
> "Per Freem" <perfreem@xxxxxxxxx> writes:
>
>
> > but since Chris's example involves expanding the language of the first
> > structure (by adding another constant to it), [...]
>
> There was no added constant, just an added element in the domain.
> Quoting his response: " Suppose B's domain is Nat U {you} and 'd_i'
> denotes i in B, for all i, and nothing denotes you in B."

yes this is true i was confusing the proof from Enderton of the same
claim (where a constant is added) with Chris's. but if adding an
element is all it takes, what would stop us from applying this
technique to show that very same theory is not \Aleph_{1}-categorical?
it shouldn't be possible since that theory /is/ \Aleph_{1}-categorical
but i'm just not sure where this technique would fail in this case?

.

Relevant Pages

  • Re: question about categoricity
    ... > but since Chris's example involves expanding the language of the first ... denotes i in B, for all i, and nothing denotes you in B." ... Prev by Date: ...
    (sci.logic)
  • Re: usage: lay vs lie vs whatever
    ... and that's no way for a language to behave ... It's necessary to know very little about the technical mechanisms ... And generally speaking, when I encounter a phrasing situation that has ... appears to be dead with lay/lie is a passive technique, ...
    (rec.arts.sf.composition)
  • Re: Is my Control a cotrol array ??
    ... Fixed size array are what's irrelevant. ... The technique should be chosen based on the ... language and understand that things like keeping Gosub in the VB.Net ... What you don't like is hearing someone's opinion that varies from ...
    (microsoft.public.vb.controls)
  • Re: Semicolon = period
    ... Word obtains its proofing and grammar rules from the language marked on the ... This technique for de-corrupting is known as "Doing a 'Maggie'", ... I sounded like a jerk -- or worse, like my wife on PMS. ... McGhie Information Engineering Pty Ltd, Sydney, Australia. ...
    (microsoft.public.mac.office.word)
  • Re: Verbose functional languages?
    ... Outside a few tiny niches like technical computing, OCaml is certainly not ... significantly updated language standard approaches. ... OTOH, I have no use for Haskell, I don't ... world" technique if anyone came to this discussion stating that they had ...
    (comp.lang.functional)