Talk:Hilbert Book Model Project/Relational Structures
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This page should only be used for discussion about the Relational Structures (subpage).
Initial remarks
[edit source]tbd
Other comments
[edit source]Comments for improved comprehension
[edit source]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.