REFLECTIONS ON MATHEMATICAL ECONOMICS IN THE ALGORITHMIC MODE

K. Vela Velupillai ()
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K. Vela Velupillai: Department of Economics, University of Trento, Via Inama 5, 381 00 Trento, Italy

New Mathematics and Natural Computation (NMNC), 2012, vol. 08, issue 01, 139-152

Abstract: Non-standard analysis can be harnessed by the recursion theorist. But as a computable economist, the conundrums of the Löwenheim-Skolem theorem and the associated Skolem paradox, seem to pose insurmountable epistemological difficulties against the use of algorithmic non-standard analysis. Discontinuities can be tamed by recursive analysis. This particular kind of taming may be a way out of the formidable obstacles created by the difficulties of Diophantine Decision Problems. Methods of existence proofs, used by the "classical" mathematician — even if not invoking the axiom of choice — cannot be shown to be equivalent to the exhibition of an instance in the sense of a constructive proof. These issues were prompted by the fertile and critical contributions to this special issue.

Keywords: Nonstandard analysis; Skolem paradox; Löwenheim-Skolem theorem; computability; Takagi function (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1142/S1793005712400091

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