Recursive pleasures

I’m much enjoying at the moment re-reading Hartley Rodgers’s Theory of Recursive Functions and Effective Computability. What prompts me to take the book off the shelf again is the treatment of constructive ordinals some two hundred pages in; but (one of the upsides of retirement) I’ve got the time to start reading from the beginning, and it is well worth spending the time doing so. The book is as good and illuminating as I remembered it as being. In fact more so, as I’m sure I didn’t really appreciate it, back in the day.

I bought my copy at the end of 1970, and paid seven pounds and nine shillings for it (the bookseller’s pencilled markings are still on the flyleaf). That was a lot more than we could afford, and I expect I didn’t fess up to my extravagance, for it would then have been about 8% of my monthly take-home pay. Such was my devotion to logic. Or my obsessive book-buying habit.

The book-buying has had to be much reduced, as we are pretty much constrained to a one-in, one-out policy (not of course, that it quite works like that). But I did get in the post today a copy of Rózsa Péter’s great Recursive Functions — the copy was relatively inexpensive and though it once belonged to the library at the National Physical Laboratory was seemingly hardly touched.  I’m not sure quite why, but I take real pleasure in having a copy at last.

Question (since the gender gap is vexing the philosophical interwebs these days): is Rózsa Péter the only woman so far who is the sole author of an indisputably significant mathematical logic book? Or am I having a senior moment and forgetting someone? (Even more run of the mill math. logic textbooks solely by women seem very few and far between: there’s Judith Roitman’s nice set theory text, and then ….?)

21 thoughts on “Recursive pleasures”

  1. This is a bit off topic but doesn’t Peter Smith’s remarks about the toy language on p32 of IGT (2nd ed) run afoul of Post-completeness? Maybe not, since the language is finite. But I doubt it. Just asking. And as for semantic arguments for incompleteness, doesn’t just about any semantic paradox give rise to a semantic incompleteness argument?

  2. If formal semantics (in Linguistics) counts, there’s Barbara Partee.

    Among recent books, there’s Formal Languages in Logic: A Philosophical and Cognitive Analysis, by Dr Catarina Dutilh Novaes, and Where is the Gödel-point hiding: Gentzen’s Consistency Proof of 1936 and His Representation of Constructive Ordinals, by Anna Horská.

  3. Daniel Nagase

    I had initially interpreted the question as referring merely to textbooks. In the context of mathematical logic more generally, I’d say Carol Karp’s Languages with Expressions of Infinite Length is an indisputably significant book.

  4. Elke Brendel co-authored the two-volume textbook ‘Grundzüge der Logik’ (1983), which has not been translated into English so far.

  5. This is another co-author, but Marian Pour-El wrote *Computability in Physics and Analysis* with Jonathan Richards.

  6. I don’t know if it counts, but Sabine Koppelberg wrote the first volume of the Monk and Bonnet’s Handbook of Boolean Algebras, which, while not exactly a textbook, is nevertheless meant to be an introduction to the subject.

  7. Speaking of constructive ordinals. I read somewhere you were writing a book on Gentzen’s consistency proofs a little like your intro to Gödel book. May I ask if it is still a live possibility ? Or is the project it completely dead ?

  8. Helena Rasiowa wrote an important book as co-author but I also saw another on non-classical logics on the shelves of our library. Perhaps it is not of undisputable importance. Wanda Szmielew wrote a book on the logical foundations of projective geometry.

    1. Yes, I was thinking of Helena Rasiowa as a female co-author; and then there there’s Zofia Adamowicz. And more recently Sara Negri has co-authored two must-read books on proof-theory with Jan Von Plato.

      1. Helena Rasiowa co-authored “The Mathematics of Metamathematics” (1963) with Roman Sikorski; but she published “An Algebraic Approach to Non-Classical Logics” (1974) which is perhaps an under appreciated book.

          1. Rasiowa also authored Introduction to modern mathematics, which is still widely used as a textbook for the first year math courses in Poland (at least 14 reprints since 1967, including one in 2013).

Leave a Comment

Your email address will not be published. Required fields are marked *

Scroll to Top