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Structures, Suppes predicates, and Boolean-valued models in physics. (English) Zbl 0899.03040

Bystrov, Peter I. (ed.) et al., Philosophical logic and logical philosophy. Essays in honour of Vladimir A. Smirnov. Dordrecht: Kluwer Academic Publishers. Synth. Libr. 257, 91-118 (1996).
The importance of questions related with axiomatization of physical theories is stated in Hilbert’s sixth problem. The authors give some examples chosen within established physical theories which indicate that the underlying models of set theory involved in the considered axiomatization of physics are striking also from the physical point of view. They work with two basic procedures to axiomatize a theory: the concept of species of mathematical structures in the sense of Bourbaki and Suppes predicates to axiomatize the theory of structures. The examples that are considered in some standard Boolean-valued models of ZFC concern the Kolmogorov-Sinai entropy, electromagnetic fields over spacetime manifolds, the integrability of a given Hamiltonian, any nontrivial characterization for chaos in dynamical systems, etc. This is the very beginning of the investigation of the physical interpretation of forcing models and the consequences of its undecidable sentences for the empirical sciences.
For the entire collection see [Zbl 0885.00036].

MSC:

03E75 Applications of set theory
00A79 Physics
03B30 Foundations of classical theories (including reverse mathematics)
78A25 Electromagnetic theory (general)
70H99 Hamiltonian and Lagrangian mechanics
03E40 Other aspects of forcing and Boolean-valued models
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