Logic & Programming

Wim Veldman taught me classical model theory and classical descriptive set theory during the 2006-2007 masterclass in logic. I continued to learn from him after the masterclass, as he had important results about Kripke models, the fan theorems, bar induction, and open induction, topics that I was and that I am still interested in. He was very kind to accept to be member of the jury for my PhD thesis defense and came to Paris for the occasion. I also remember receiving a review of a paper – a very objective one – that was expressly signed by him, although it was supposed to be an anonymous review.

Wim was in fact an intuitionistic mathematician, in the original sense of the word, a student of J. J. de Iongh, who learned about intuitionism from L. E. J. Brouwer. This is one of the aspects that made Wim a very interesting teacher of model theory and descriptive set theory. During the classes, he would warn us the students of an incoming powerful use of the axiom of choice in a proof of a theorem, so that we are aware of the danger, or reassure us in case the choice principle were only used to deal with a countable language. When the law of excluded middle were necessary, he would look upwards and evoke the Book of God, mockingly (although he was deeply religious I think), to point out the gravity of the act of evoking the LEM.

Model theory became more constructive for me thanks to these clarifications. Model theory is constructive, as a matter of fact, at least in the sense that it contains a wealth of counter-models that a constructive mathematician could use, as a guide, as a complement, while looking for constructive proofs or definitions.

Another aspect that made Wim an excellent teacher was his teaching technique. He had a very developed sense of measure of how much information to give out. He wanted to draw our full attention to completing the picture he wanted to transmit. Sometimes, he would put his hands behind his back, look at us and pose a question, and I had the impression that he was hiding the answer in his closed fist, and that we only needed to guess what the answer was. At the exams, the question posed did not require to prove or disprove a particular statement; the question asked to make up ones mind about the truth of the statement, and then either prove it or prove its negation.

I last saw Wim a couple of years ago in Nijmegen. We met up for dinner in the city center and we walked across the Waal River and back. He mentioned in passing his recent long stay at a hospital, but it had not stopped him from taking his bike to come to meet me and having very long and enthusiastic discussion on logic, life, music and literature. We had exchanged a few emails since then, one on the intuitionistic arithmetical hierarchy. I had been following his latest papers as a reviewer or on arXiv. The last one I read was a beautiful and elementary account of the basic ideas around intuitionism, Intuitionism: an inspiration?, intuitionism in the original sense of the word.

He passed away on November 30, 2024. My condolences to his family and friends. I will continue to gladly remember Wim.

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