Joel David Hamkins: The Math Tea argument-must there be numbers we cannot describe or define?

[@NikolajKuntner]

Thanks for this. I find myself coming back to that MO post on the definability definability every now and again. :)

[@NoNTr1v1aL]

Absolutely amazing video! Could you please suggest books on mathematical logic specifically in the work of Saharon Shelah and Hrushovski?

[@drewduncan5774]

Try Set Theory by Thomas Jech.

[@davidtaffs9370]

I suspect (infinite) definitions are uncountable, you can map them one-to-one with real numbers. Of course finite definitions are finite.

[@pmcate2]

@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?

[@LaureanoLuna]

Addressing your first question; consider that the only nonlogical symbols of the language associated with the structure are "