“…After a brief stop in the nineteenth century to consider the culture of research mathematics in 1860s Prussia, the book moves into the twentieth century with an examination of the historical context within which the Axiom of Choice was developed and a paper discussing Anatoly Vlasov’s adaptation of the Boltzmann equation to ionized gases. …”
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“…Generalizations of Tarski’s theorem by Merrifield and Stein and Abian’s proof of the equivalence of Bourbaki–Zermelo fixed-point theorem and the Axiom of Choice are described in the setting of posets. …”
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“…As a fairly frequent form of the Axiom of Choice about relatively simple structures (posets), Hausdorff’s Maximal Chain Principle appears to be little amenable to computational interpretation. …”
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“…Cohen’s first model is a model of Zermelo–Fraenkel set theory in which there is a Dedekind-finite set of real numbers, and it is perhaps the most famous model where the Axiom of Choice fails. We force over this model to add a function from this Dedekind-finite set to some infinite ordinal κ. …”
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“…The appendix establishes the equivalence of the Lemma of Zorn and the Axiom of Choice, and it contains a proof of Tychonoff's theorem. …”
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