Talk:Hilbert Book Model Project/Relational Structures

This page should only be used for discussion about the Relational Structures (subpage).

Initial remarks

tbd

Other comments

Comments for improved comprehension

The first 26 axioms use pure set mathematical operators and can be well understood this way. At the 27th axiom multiple additional details appear, which should be more clearly described:

The set L appears and seems to be the lattice as a whole.
The set S appears, which is unclear to me.
The "<" relational operator appears, which seems to be used as conventional "lower as" sorting operator.

With the last interpretation the resulting x = a or x = (a intersection with p) would be wrong. Hence there is something different told, what needs better explanation.

Regarding the week modular compared to the modular lattice the naming sounds questionable:

The modular lattice looks to be linear in a way that the union operation adds nothing to the result, what is not already included in the parts.
Instead the week modular lattice seems to be non-linearly productive in the way that any union operation produces more than the sum of parts.

Naming such a behavior as week seems to be not well defined to me.

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