Autograph letter signed to Martin Davis
Publisher Information: Union, ME: 1949.
Kleene, Stephen C. (1904-94). Typed letter signed (with a few manuscript additions) to Martin Davis (1928-2023). 1+ pages on single sheet. Union, Maine, 7 October 1949. 280 x 218 mm. Staple-holes in upper left corner, light wear and soiling but very good.
Writing from his farm in Maine, Kleene continues his epistolary discussion of Davis’s graduate work and his own forthcoming book, and corrects an error in one of his published papers:
"I do not go to Europe until January. I found your letter interesting. I certainly agree that it is an interesting project to extend the hierarchy of elementary predicates into the second number class. There is enough unexplored territory there to provide material for more than one paper I am sure . . .
"My book will not go into this beyond essentially the point you describe in the first paragraph of your letter [not present here]. The proof of Theorem XI of my 1943 paper is given. It is implicit in the method of treatment in my book that the extension can be made to all ordinals <2 (this is because the form of Theorem XI provides only for limiting a sequence of orders obtained from successive alternating quantifications). There is certainly a more general form of Theorem XI; but I do not attempt to go into this in the book . . .
"There is an error in my paper 'Forms of Predicates in the Theory of Constructive Ordinals' which perhaps you have already discovered . . . I quote the correction as I have it written up for publication in the bibliography of my book . . . [correction follows]
"The results you mention as coming out of your work on Hilbert’s tenth problem sounds interesting, though I am not sure if I understand correctly what you mean by a “primitive recursive set” of Diophantine equations."
Davis’s doctoral thesis on Hilbert’s tenth problem, On the Theory of Recursive Unsolvability (1950), led to the MRDP theorem for Diophantine sets.
Book Id: 51655Price: $1,250.00