@12:50 you say that A not being periodic implies Leibnizian. But doesn't the inclusion of < with the usual interpretation already suffice? Also, how is definability affected by infinitary logic? For whatever reason my intuition is that languages allowing countably long sentences could have point-wise definability for models with cardinality of the reals, but for models of greater size there would still be undefinable elements. Also, @21:32 by V do you mean the von Neumann universe?
Thanks for this.
I find myself coming back to that MO post on the definability definability every now and again.
:)
Absolutely amazing video! Could you please suggest books on mathematical logic specifically in the work of Saharon Shelah and Hrushovski?
Try Set Theory by Thomas Jech.
I suspect (infinite) definitions are uncountable, you can map them one-to-one with real numbers. Of course finite definitions are finite.
@12:50 you say that A not being periodic implies Leibnizian. But doesn't the inclusion of < with the usual interpretation already suffice? Also, how is definability affected by infinitary logic? For whatever reason my intuition is that languages allowing countably long sentences could have point-wise definability for models with cardinality of the reals, but for models of greater size there would still be undefinable elements. Also, @21:32 by V do you mean the von Neumann universe?
Addressing your first question; consider that the only nonlogical symbols of the language associated with the structure are "