By A. Ehrenfeucht, V.W. Marek, M. Srebrny
Andrzej Mostowski was once one of many major twentieth century logicians. His legacy is tested during this quantity of papers committed either to his impressive medical history and to the reminiscence of him as an excellent researcher, instructor, organizer of technological know-how and individual. Professor Mostowski pioneered and mastered many components of mathematical common sense. His contributions spanned set conception, recursion concept, and version conception - the spine of the principles of arithmetic. the total distinct bibliography of Mostowski's writings is incorporated. for a few years after WWII and particularly within the overdue sixties and until eventually his premature dying in 1975, Warsaw, the place he led the centre of foundational reports, was once a spot the place many best logicians visited, studied, and commenced their occupation. Their stories shape an enormous a part of this quantity, trying to convey again the intense achievements and character of Mostowski.
Anyone eager to see the roots of present purposes of common sense, be it in arithmetic, computing device technology or philosophy, will locate during this selection of articles lots of precious, stimulating and encouraging fabric either in technological know-how and in regards to the social atmosphere within which technological know-how is made.
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Extra resources for Andrzej Mostowski and Foundational Studies
I thought: he can forgive me all sorts of behavior, long hair, pink shirts, etc. – but this? Fortunately, Professor Mostowski had a sense of humor about it. The excitement with forcing abated; we were moving on. Slowly, but unmistakably, Mostowski’s seminars were moving in a different direction; that of formalized secondorder theories. Let me first discuss second-order arithmetic. Second-order arithmetic is, in fact, a theory of natural numbers and their subsets. It can be formalized in first-order logic.
Even stronger, Gödel announced (the proof was finally presented by Bernays and Hilbert a couple of years later) that every axiomatizable theory containing arithmetic is incomplete and that the arithmetized version of Liar Paradox (in the form “I am unprovable”) is undecidable for such theories. But Continuum Hypothesis is a concrete statement, of obvious mathematical meaning. We can explain it easily to every mathematician. To claim that such statement may be undecidable was really revolutionally at the time.
But there are deeper and even more profound reasons. When we limit second-order arithmetic to some parts (too technical to be discussed here), it turns out that we capture some of the most fundamental theorems of mathematics (for instance the König theorem on finitely splitting trees or the Baire Category Theorem). Amazing results of Harvey Friedman, Jeffrey Remmel, Stephen Simpson and their students have shown that, in fact, the number of these important fragments appears to be limited. This is the area of Reverse Mathematics.
Andrzej Mostowski and Foundational Studies by A. Ehrenfeucht, V.W. Marek, M. Srebrny