David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Journal of Symbolic Logic 62 (2):493-505 (1997)
The role played by real-valued functions in functional analysis is fundamental. One often considers metrics, or seminorms, or linear functionals, to mention some important examples. We introduce the notion of definable real-valued function in functional analysis: a real-valued function f defined on a structure of functional analysis is definable if it can be "approximated" by formulas which do not involve f. We characterize definability of real-valued functions in terms of a purely topological condition which does not involve logic
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