Year: 2011
Type: preprint
Abstract: It is known that the theory of any class of normed spaces over the reals that includes all spaces of a given dimension d > 1 is undecidable, and indeed, admits a relative interpretation of second-order arithmetic. The notion of a normed space makes sense over any ordered field of scalars, but such a strong undecidability result cannot hold in the more general case. Nonetheless, we find that the theory of any class of normed spaces in the more general sense that includes all spaces of a given dimension d > 1 over some ordered field admits a relative interpretation of Robinson's theory Q and hence is undecidable.
Source: arXiv (Cornell University)
Author: Arthan, Rob
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1641997338