1. Guiness Book of World Records, youngest professor, 18, Stanford University.
2. Senior Distinguished Research Award, Ohio State University, April 1982.
3. Alan T. Waterman Award, for “his revitalization of the foundations of mathematics, his penetrating investigations into the Gödel incompleteness phenomena, and his fundamental contributions to virtually all areas of mathematical logic,” by the National Science Foundation, 1984.
4. Named among “the top 100 scientists in the U.S. under 40” by Science Digest, December 1984.
5. Invited by President Ronald Reagan to a luncheon at the White House “in recognition of outstanding scientists, mathematicians and engineers,” held February 12, 1985.
6. Distinguished University Professor , Ohio State University, 1987 – 2012. Emeritus 2012 –
7. Guggenheim Fellowship, “Studies in the Foundations of Mathematics,” October 1986 – August 1987.
8. Gödel Lecture, Issues in the Foundations of Mathematics, Annual meeting of the ASL, Las Vegas, Nevada, June 1-4, 2002, 1 hour.
9. Rademacher Lectures, Demonstrably necessary uses of abstraction, Mathematics Department, University of Pennsylvania, September 16-20, 2002, 4 one hour lectures.
10. Nineteenth Annual Tarski Lectures, Interpretations of Set Theory in Discrete Mathematics and Informal Thinking, Department of Mathematics, University of California, Berkeley, 3 one hour lectures.
11. Institutional Honorary Doctorate, University of Ghent, Ghent, Belgium, September 4, 2013.