[FOM] first/second order logic

[sambin at math.unipd.it]

  Quoting Richard Heck <richard_heck at brown.edu>:

> On 11/6/19 10:27 AM, Harvey Friedman wrote:
>
>> QUESTION. Is there an interesting completeness theorem for  
>> nontrivial fragments of second order logic? Obviously, first order  
>> logic is a nontrivial fragment that does have a completeness  
>> theorem. But what if we look at SIMPLE fragments of second order  
>> logic. Maybe there are really interesting such with a completeness  
>> theorem. Or if there has been a good start on this, then how far  
>> can it be pushed?
>
>   Well, predicative second-order logic is natural and is complete,  
> isn't it, with respect to some reasonably natural notion of what a  
> model is? 

Dear Riki,
what do you have in mind for "predicative second-order logic"? And  
hence also the question: what is the natural notion of model for it?
Thank you for attention
Giovanni (Sambin)
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