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arXiv · 2506.02029

Axioms of Quantum Mechanics in light of Continuous Model Theory

Boris Zilber
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Abstract

The aim of this note is to recast somewhat informal axiom system of quantum mechanics used by physicists (Dirac calculus) in the language of Continuous Logic. We note an analogy between Tarski's notion of cylindric algebras, as a tool of algebraisation of first order logic, and Hilbert spaces which can serve the same purpose for continuous logic of physics.

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Boris Zilber. 2025-05-30. Axioms of Quantum Mechanics in light of Continuous Model Theory. https://arxiv.org/abs/2506.02029

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