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If the absence of (3) is stressed, the epithet "without identity" is added, in contrast to first-order logic with identity, in which (3) is also included.
Without identity documents, employers cannot hire us.
Morente called himself "a cantaor without identity".
Analogy means similarity of properties or relations without identity.
And without identity papers, they can do virtually nothing.
He finds himself somehow without identity in this place, which is some distance from his home.
Without identity documents they face arrest and imprisonment as illegal immigrants.
The Internet obliges by offering simulated sex without intimacy, without identity and without fear of infection.
Pallid, friendless, deprived of experience, he is, like a character in a Paul Auster novel, almost without identity.
Similar(2)
Hence, the conjunction has a model in the sense of logic-without-identity if and only if F has a model in the sense of logic-with-identity; and the completeness of elementary logic (with identity) can thus be inferred.
Thus utilitarianism does not demand that one live without identity-conferring commitments at all, but that one live with utilitarian identity-conferring commitments.
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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