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Suppes predicates for classical physics. (English) Zbl 0847.03007

Echeverria, Javier (ed.) et al., The space of mathematics. Philosophical, epistemological, and historical explorations. Revised papers from a symposium on structures in mathematical theories, Donostia/San Sebastian, Basque Country, Spain, September 1990. Berlin: Walter de Gruyter. Grundlagen der Kommunikation und Kognition. 168-191 (1992).
We have a threefold aim in the present paper: first, we wish to exhibit a unified treatment for the mathematical structures underlying what one usually calls in a loose way “classical physics”, or “first-quantized physics”, or even “classical field theory”. That means, we are going to discuss Hamiltonian mechanics, electromagnetic theory in the Maxwell formulation, general relativity, the classical aspects of gauge field theory and the theory of the Dirac electron, again seen as a field theory. Such theories can also be looked upon as “first quantized theories” (but for Hamiltonian mechanics), as, for example, we can suppose that Einstein’s gravitation is the depiction of the motion of a single graviton whose associated wave function is a nonlinear perturbation of a flat background metric field.
Now, since the mathematical structures we are going to deal with are set-theoretic constructs, we are going to develop them within a standard framework, such as the Zermelo-Fraenkel theory; that will be done with the help of Suppes predicates.
Finally, we wish to lay the groundwork for a systematic exploration of the consequences of metamathematical phenomena within theoretical and mathematical physics. We are especially interested in the consequences of, say, undecidability results that might appear within a given physical theory, or in the dependence of a given physical theory on a particular axiomatic system.
For the entire collection see [Zbl 0839.00019].

MSC:

03B30 Foundations of classical theories (including reverse mathematics)
00A79 Physics
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