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Gödel, Kurt | The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis with the Axioms of Set Theory

  • Second printing, originally published in 1940. From the library of Nobel Prize-winning biologist Sydney Brenner, with his ownership signature and the date “14 November 1952” on the cover.

    The present mathematical model, better known by its short title, The Consistency of the Continuum Hypothesis, “is a classic of modern mathematics. The continuum hypothesis, introduced by mathematician George Cantor in 1877, states that there is no set of numbers between the integers and real numbers. It was later included as the first of mathematician David Hilbert's twenty-three unsolved math problems, famously delivered as a manifesto to the field of mathematics at the International Congress of Mathematicians in Paris in 1900. In The Consistency of the Continuum Hypothesis Gödel set forth his proof for this problem” (De Gruyter blurb).

    Sydney Brenner (1927-2019) was a leader in the field of genetics almost from the moment he received his doctorate at Oxford in 1954. He joined Francis Crick’s laboratory in 1956, and they did groundbreaking research on how DNA is decoded by cells. Brenner proposed that the nucleotides which comprise DNA (adenine, guanine, thiamine and cytosine) are read by the cell in sets of three called codons, with each codon representing an amino acid (for example, three adenines in a row is the codon for the amino acid lysine). A gene is simply a string of codons that directs the production of a protein molecule from individual amino acids. He also correctly predicted the existence of messenger RNA, the molecule that carries the genetic code from the nucleus to the ribosomes, where the translation process occurs.

    Following this work, it was Brenner’s efforts to establish a new laboratory organism for the study of genetics that led to his Nobel Prize. “Beginning in 1965, he began to lay the groundwork to make C. elegans, a small, transparent nematode, into a major model organism for genetics, neurobiology and developmental biology research. As a direct result of his original vision, this tiny worm became the first animal for which the complete cell lineage and entire neuronal wiring were known. Today, more than 1,000 investigators are studying C. elegans, and Brenner’s work was further honored when a closely related nematode was named Caenorhabditis brenneri” (Salk Institute biography).

  • Princeton, NJ, London & Oxford: Princeton University Press; Humphrey Milford; Oxford University Press, 1951.

    Octavo. Original orange wrappers printed in black. Small pencilled price mark to the upper wrapper. Spine and edges of wrappers tanned, some light rubbing. A very good copy.