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arithmetization

Definitions

from The Century Dictionary.

  • noun The process by which any part of mathematics is so recast as to be made to depend only upon purely arithmetical concepts, to the exclusion of all measurement.

Etymologies

Sorry, no etymologies found.

Examples

  • This follows the kind of definitions used in the arithmetization of analysis of the preceding century, in particular, Dedekind's earlier construction of real numbers as bounded classes of rational numbers.

    Logical Constructions

  • He forcefully shows the difference between the late nineteenth century arithmetization of analysis and the early twentieth century axiomatic-algebraic approach.

    Mathematical Style

  • Providing an explicit, rigorous, and fruitful definition of the real numbers constitutes a major step towards completing the arithmetization of analysis.

    Dedekind's Contributions to the Foundations of Mathematics

  • The finite (and perhaps, surprisingly small) number of symbols and the availability of recursive functions conjure the thought that an arithmetization of the syntax of CL could be attempted.

    Combinatory Logic

  • With the work of Gödel and Tarski, paradoxical arguments were reshaped into fixed point results, while the semantic conception of truth, the formalization of semantics and the arithmetization of syntax yielded firm grounds for systematic metamathematical investigations.

    Paradoxes and Contemporary Logic

  • In the proof of this theorem, Tarski applies arithmetization and diagonalization, hence following the Gödelian pattern.

    Paradoxes and Contemporary Logic

  • Carnap, and Goedel elsewhere presumably, similarly undercut the distinction, according to Grattan-Guinness, with the arithmetization of syntax as presented in Logical Syntax.

    Words and Other Things

  • More directly, Dedekind's essay was tied to the arithmetization of analysis in the nineteenth century ” pursued by Cauchy, Bolzano,

    Dedekind's Contributions to the Foundations of Mathematics

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