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.
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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 Linsky, Bernard 2009

He forcefully shows the difference between the late nineteenth century arithmetization of analysis and the early twentieth century axiomaticalgebraic approach.
Mathematical Style Mancosu, Paolo 2009

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 Reck, Erich 2008

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 Bimbó, Katalin 2008

With the work of GÃ¶del 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 Cantini, Andrea 2007

In the proof of this theorem, Tarski applies arithmetization and diagonalization, hence following the GÃ¶delian pattern.
Paradoxes and Contemporary Logic Cantini, Andrea 2007

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

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 Reck, Erich 2008
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