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Following this notation, we can formalize rigid existential dependence as follows: "□(Ex → Ey)", which can be read as "x rigidly depends for its existence on y", or alternatively "x rigidly necessitates y".
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Alternatively, a proponent of the modal-existential account could simply bite the bullet and insist that every contingent entity does rigidly depend for its existence on necessary existents.
So object x is strongly rigidly dependent on object y if x depends for its existence on y and y is not a proper part of x.
We have mentioned one example of rigid existential dependence, namely, sets ontologically depending on their members (more precisely, a set depends rigidly on the very members it has, i.e., any change in a set's members will change the set itself).
Timings were not rigidly fixed and depended on the availability of electricity, the weather, and the household engagements of women.
"It all depends on how rigidly you want to read the law," he replied, according to an audio recording from the Distressed Real Estate Summit on May 13 at a downtown hotel.
One is hierarchical, rigidly organized, likes spit and polish, and depends on a lot of grunts to do most of the work.
An immediate implication of (ID-EX) in conjunction with (EDR) is that if x depends for its identity upon y, then x is rigidly existentially dependent upon y (although not necessarily vice versa, of course).
What the matrix reveals is that the expression 'I' rigidly designates different individuals, depending on the context in which it is used.
The play depends upon an intimate bond between actor and audience hard to achieve in this rigidly geometrical theatre.
To be successful, the approach depends on well-organized dialogue between decision makers at many levels, which would be culture shock for the rigidly hierarchical executive branch.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com