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

T.Forster at dpmms.cam.ac.uk T.Forster at dpmms.cam.ac.uk
Sun Dec 2 05:39:14 EST 2012

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  
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