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I expect the downvotes here but it is important.

It doesn’t matter if you get there through Trakhtenbrot or Rice.

Codd’s normal form is a projection, it will turn your fancy model logic into classic logic.

IMHO it is always something to look for to use as a default, but fails if it is a hard requirement.

One classic way to describe the problem is the White king and Alice.

> ‘I see nobody on the road,’ said Alice.

> ‘I only wish I had such eyes,’ the King remarked in a fretful tone. ‘To be able to see Nobody! And at that distance, too! Why, it’s as much as I can do to see real people, by this light!’

Codd added nulls to handle unknowns or missing data.

The proper use of them is a complex subject. But they are required if you care about semantic correctness and not just logical validity in many cases.

Diaconescu-Goodman-Myhill theorem[0] will show the equivalence between PEM, finite indexes, and choice

[0] https://ncatlab.org/nlab/show/Diaconescu-Goodman-Myhill+theo...



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