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(4.1) is proved by analyzing the set-theoretic definition of H ω1) and showing that it can be "internally" formulated in L ω1,ω1).
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But it seems clear that (i) we humans are capable of formulating internally consistent mathematical theories (and of knowing that they are internally consistent), and (ii) being able to do this does not require us to have any sort of information-transferring contact with the abstract objects that the theories in question are about.
The process in each cycle is formulated as a switched system with internally forced switching instants.
Motivated by injection molding processes, the multi-phase batch process in each cycle is formulated as a switched system with internally forced switching instant.
Substance metaphysics proceeds from the intuition first formulated by the pre-Socratic Greek philosopher Parmenides that being should be thought of as simple, hence as internally undifferentiated and unchangeable.
They can be simply formulated.
A new plan was formulated.
A plan was hastily formulated.
So he formulated a plan.
It have been formulated.
They have been masterfully formulated.
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CEO of Professional Science Editing for Scientists @ prosciediting.com