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The Prehistory of Infinitary Logic: 1885–1955

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Structures and Norms in Science

Part of the book series: Synthese Library ((SYLI,volume 260))

Abstract

Traditionally, logic was restricted to proofs having a finite number of steps and to expressions of finite length. Around 1954–56, infinitely long formulas entered the mainstream of mathematical logic through the work of Henkin, Karp, Scott, and Tarski. Soon Hanf and Tarski used such logics to settle negatively the 30-year-old problem of whether the first strongly inaccessible cardinal is measurable, a result Tarski communicated to the first LMPS congress in 1960. Infinitary logic continues to be fertile in unexpected ways, as shown by Kolaitis at the present congress.

History is difficult... because the connections that matter are usually numerous, often hidden, and then subsequently neglected.

S. Mac Lane [33, 441]

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Author information

Authors and Affiliations

  1. Department of Mathematics, McMaster University, Hamilton, Ontario, Canada

    Gregory H. Moore

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  1. Gregory H. Moore
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Editor information

Editors and Affiliations

  1. University of Florence, Italy

    Maria Luisa Dalla Chiara

  2. University of Amsterdam, The Netherlands

    Kees Doets

  3. University of Milan, Italy

    Daniele Mundici

  4. University of Amsterdam, The Netherlands

    Johan Van Benthem

  5. Stanford University, USA

    Johan Van Benthem

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© 1997 Springer Science+Business Media Dordrecht

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Moore, G.H. (1997). The Prehistory of Infinitary Logic: 1885–1955. In: Chiara, M.L.D., Doets, K., Mundici, D., Van Benthem, J. (eds) Structures and Norms in Science. Synthese Library, vol 260. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0538-7_7

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  • DOI: https://doi.org/10.1007/978-94-017-0538-7_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4787-8

  • Online ISBN: 978-94-017-0538-7

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