[FOM] criteria for the existence of infinite models of FO theories

[T.Forster at dpmms.cam.ac.uk]

Related to this is the question of the minimal logical complexity of an 
axiom of infinity (an axiom that has only infinite models) There is a JSL 
article by Parlamento and Policriti about this which i cannot locate from 
my transit lounge in Guanzhou. I think they have one that is 
universal-existential, and this is obviously best possible unless one has 
very fine vision. (For example, their fmla is unstratified .... and it is, 
i believe, open whether or not a stratified universal-existential sentence 
- or even a scheme - can be found)

On Dec 1 2012, Charlie wrote:

>	    Is this the same question as before?  I'm not sure.
>
> If so, one way would be to incorporate these three simple sentences as 
> axioms (or their conjunction):
>
>1) Ax~(Fxx);
>2) AxAyAz(Fxy & Fyz --> Fxz);
>3) AxEy(Fxy).
>
>Charlie Silver
>
>On Jul 30, 2012, at 4:22 PM, Andrei Popescu <uuomul at yahoo.com> wrote:
>
>> Dear FOM subscribers,
>> 
>> I am searching for (preferably lightweight) syntactic criteria for a 
>> first-order theory to admit infinite models. I would appreciate any 
>> pointers to results in the literature.
>> 
>> All the best, 
>>    Andrei Popescu  
>> _______________________________________________
>> FOM mailing list
>> FOM at cs.nyu.edu
>> http://www.cs.nyu.edu/mailman/listinfo/fom
>
>_______________________________________________
>FOM mailing list
>FOM at cs.nyu.edu
>http://www.cs.nyu.edu/mailman/listinfo/fom
>