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I have several times come across the name P C Gilmore, and even made use of a publication by her, or him, viz. "The consistency of partial set theory without extensionality", which was published in Tomas Jech (ed): Axiomatic Set Theory, Part 2, American Mathematical Society, 1974, 147-153.

May someone reveal what the initials "P" and "C" stand for?

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Mathematics Genealogy Project, which I see is a service of the NDSU Department of Mathematics, in association with the American Mathematical Society, suggests that his name is Paul Carl Gilmore:

https://www.mathgenealogy.org/id.php?id=49610

and this seems confirmed by Mathscinet:

https://mathscinet.ams.org/mathscinet/MRAuthorID/73705

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Definetively it is Paul Carl Gilmore, he passad away on April 8, 2015, here an obituary.

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