Axiomatic set theory
by Patrick Suppes · first published 1960
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2012–2024first – last mentioned
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…"On other hand if you can show that your favorite Neveu calculus can be proved sound according to some computable logic, that would indeed be helpful." Nonsense. Neveu is based just on set theory, axiomatic set theory if you wish, the foundations as in Bourbaki if you wish, or P. Suppes, essentially the same as all of math for the past 100 years or so. For the importance of that material, there is nothing anyone should…
…Russell, etc. there was an effort to redefine everything in mathematics starting with just sets. Then everything was constructed starting with just the low level ideas of sets. The serious result was axiomatic set theory, e.g., as in P. Suppes, Axiomatic Set Theory. So, numbers, functions, calculus, lines, planes, spheres, groups, rings, fields, vector spaces. etc. were all defined based on sets. And similarly for Lebesgue's…
on “Frequentism and Bayesianism: A Practical Introduction” ↗Part I I tried a grad math department and didn't like it: (1) In a course in real analysis, early on the prof discussed some set theory. The summer before I'd had an NSF thing in axiomatic set theory, Suppes, von Neumann, an appendix in Kelley, etc. His first test had a problem, and at the last minute I saw a solution and wrote it down. He called me on the carpet -- nasty guy. I apologized for using…
on “Designing a Business Card in LaTeX” ↗I'm reminded of the textbook Axiomatic Set Theory by Suppes, which has on page 137 a proof that 3 + 1 = 4.
on “A Simple Proof That Pi Is Irrational” ↗…For more, there is the elegant, long popular, P. Halmos Naive Set Theory, now available in PDF, LaTeX, etc. For more there is the appendix to J. Kelley, General Topology. For more there is P. Suppes, Axiomatic Set Theory. For more, sure you want more????
on “This Message Does Not Exist” ↗1. Axiomatic Set Theory by Suppes 2. Solar Lottery by Philip K. Dick
on “Ask HN: What book are you reading?” ↗"(I'm into abstract and theoretical math)" So what is a good Linear Algebra textbook from that perspective? Assume someone has completed a course in Axiomatic Set Theory and is conversant with proofs etc, but now wants to get into Linear Algebra. Any textbook suggestions?
on “A First Course in Linear Algebra” ↗