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Topic: Can L(<) be the language of the naturals?
Replies: 35   Last Post: Sep 10, 2013 2:12 AM

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Peter Percival

Posts: 1,302
Registered: 10/25/10
Re: Can L(<) be the language of the naturals?
Posted: Sep 1, 2013 1:37 PM
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David Hartley wrote:
> In message <52236CD3.1030800@osu.edu>, Jim Burns <burns.87@osu.edu> writes
>> If I say that I have a set with a semi-infinite,
>> discrete, linear order, (N, <), is that enough to
>> define the naturals?

>
> I'm afraid not. Thee are many other orderings satisfying your axioms.
> E.g. N + Z - i.e. a copy of N followed by a copy of Z.


Also, there is no recursive set of first order axioms that will capture
just the natural numbers.

--
Sorrow in all lands, and grievous omens.
Great anger in the dragon of the hills,
And silent now the earth's green oracles
That will not speak again of innocence.
David Sutton -- Geomancies


Date Subject Author
9/1/13
Read Can L(<) be the language of the naturals?
Jim Burns
9/1/13
Read Re: Can L(<) be the language of the naturals?
Jim Burns
9/1/13
Read Re: Can L(<) be the language of the naturals?
David Hartley
9/1/13
Read Re: Can L(<) be the language of the naturals?
Peter Percival
9/1/13
Read Re: Can L(<) be the language of the naturals?
Virgil
9/1/13
Read Re: Can L(<) be the language of the naturals?
Peter Percival
9/1/13
Read Re: Can L(<) be the language of the naturals?
Virgil
9/2/13
Read Re: Can L(<) be the language of the naturals?
albrecht
9/6/13
Read Re: Can L(<) be the language of the naturals?
albrecht
9/6/13
Read Re: Can L(<) be the language of the naturals?
Robin Chapman
9/6/13
Read Re: Can L(<) be the language of the naturals?
Tucsondrew@me.com
9/6/13
Read Re: Can L(<) be the language of the naturals?
LudovicoVan
9/6/13
Read Re: Can L(<) be the language of the naturals?
Tucsondrew@me.com
9/7/13
Read Re: Can L(<) be the language of the naturals?
albrecht
9/6/13
Read Re: Can L(<) be the language of the naturals?
Michael F. Stemper
9/7/13
Read Re: Can L(<) be the language of the naturals?
albrecht
9/6/13
Read Re: Can L(<) be the language of the naturals?
FredJeffries@gmail.com
9/7/13
Read Re: Can L(<) be the language of the naturals?
albrecht
9/7/13
Read Re: Can L(<) be the language of the naturals?
FredJeffries@gmail.com
9/8/13
Read Re: Can L(<) be the language of the naturals?
albrecht
9/6/13
Read Re: Can L(<) be the language of the naturals?
Robin Chapman
9/6/13
Read The decimals by Stevin
Brian Q. Hutchings
9/7/13
Read Re: Can L(<) be the language of the naturals?
albrecht
9/6/13
Read Re: Can L(<) be the language of the naturals?
LudovicoVan
9/7/13
Read Re: Can L(<) be the language of the naturals?
albrecht
9/7/13
Read Re: Can L(<) be the language of the naturals?
LudovicoVan
9/8/13
Read Re: Can L(<) be the language of the naturals?
albrecht
9/8/13
Read Re: Can L(<) be the language of the naturals?
LudovicoVan
9/8/13
Read Re: Can L(<) be the language of the naturals?
albrecht
9/9/13
Read Re: Can L(<) be the language of the naturals?
LudovicoVan
9/10/13
Read Re: Can L(<) be the language of the naturals?
albrecht
9/1/13
Read Re: Can L(<) be the language of the naturals?
Jim Burns
9/2/13
Read Re: Can L(<) be the language of the naturals?
Shmuel (Seymour J.) Metz
9/2/13
Read Re: Can L(<) be the language of the naturals?
Shmuel (Seymour J.) Metz
9/2/13
Read Re: Can L(<) be the language of the naturals?
Shmuel (Seymour J.) Metz
9/2/13
Read Re: Can L(<) be the language of the naturals?
Peter Percival

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