How many important logicians did NOT receive doctoral degrees?

Question

I can think of three. Saul Kripke quite famously could only be begrudged to finish his undergraduate degree at Harvard before being hired as a full professor. Donald Martin (the set theorist of Martin's Axiom fame) seems to have been hired into professorship out of a post-baccalaureate fellowship, without pursuing graduate study. Finally, I can't find evidence that Chaitin ever got any graduate degrees.

Are there other famous examples of great logicians or mathematicians making it into the academy while skipping over the PhD? Examples from before the era of the modern academic degree structure are not interesting for the purpose of this inquiry.

One of my professors told me that these days, someone in a similar situation would likely be put into a no-effort PhD program until the residency requirements are met, with some important publication or another of theirs being declared a "dissertation." None of the professors I asked this to could think of a fourth example. Thus, it seems the no-doctorate logician is a dying breed, one worth examining and cataloguing.

Answer 1

Thoralf Skolem could perhaps be counted as a quasi example of that. He did not enroll as a PhD candidate before becoming a docent and a member of the Norwegian Academy of Science and Letters, and it seems that he still needed some convincing from his colleagues in order to actually submit a thesis, several years later. When he finally defended it, his formal supervisor, Axel Thue, had already been deceased for no less than four years.

Do note, though, that this could actually be seen as a century-old example of the claim made by your professor.

Answer 2

Regarding "logicians or mathematicians", Karl Weierstrass made it "into the academy while skipping over the PhD", though he did eventually receive an honorary doctorate.

From William Dunham's The Calculus Gallery:

He followed a nontraditional route to prominence. His student years had been those of an underachiever, featuring more beer and sword play than is normally recommended. At age 30 Weierstrass found himself on the faculty of a German gymnasium (i.e., High School) far removed from the intellectual centers of Europe. [...]

In 1854 this unknown teacher from an unknown town published a memoir on Abelian integrals that astonished the mathematicians who read it. It was evident that the author, whoever he was, possessed an extraordinary talent. Within two years, Weierstrass had secured a position at the University of Berlin and found himself on one of the world's great mathematical faculties. His was a truly Cinderella story.