[FOM] first/second order logic
sambin at math.unipd.it
sambin at math.unipd.it
Fri Nov 8 08:39:04 EST 2019
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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