Re: Is peano arithmetic inconsistent under the intended interpretation?

From: Frederick Williams <"Frederick Williams"@antispamhotmail.co.uk.invalid>
Date: Sat, 08 Mar 2008 15:31:59 GMT

Newberry wrote:

On Mar 8, 3:03 am, Aatu Koskensilta <aatu.koskensi...@xxxxxxxxx>
wrote:

On 2008-03-08, in sci.logic, Newberry wrote:

For example expressing that there are no infinite numbers and adding
it as a axiom would exclude the non- standard models.

Certainly if we adopt more expressive logical apparatus we can
characterise the standard model. What does that have to do with
"inconsistency of Peano arithmetic under the intended interpretation"?

In the intended interpretation there are no infinite numberes. If we
add axioms that explicitly outlaw infinite numberes and thus the non-
standard models, we get an inconsistency.

Second order PA is categorical: the sole model is the intended one, no
inconsistency.

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References:
- Is peano arithmetic inconsistent under the intended interpretation?
  - From: Newberry
- Re: Is peano arithmetic inconsistent under the intended interpretation?
  - From: David C . Ullrich
- Re: Is peano arithmetic inconsistent under the intended interpretation?
  - From: Newberry
- Re: Is peano arithmetic inconsistent under the intended interpretation?
  - From: Aatu Koskensilta
- Re: Is peano arithmetic inconsistent under the intended interpretation?
  - From: Newberry
- Re: Is peano arithmetic inconsistent under the intended interpretation?
  - From: Aatu Koskensilta
- Re: Is peano arithmetic inconsistent under the intended interpretation?
  - From: Newberry

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