5 papers
Approximation of structures:local and global
Boris Zilber
We provide a mathematically rigorous definition of local approximation and demonstrate its applicability to some interesting classes of structures. In particular, we prove that any…
Dirac - von Neumann axioms in the setting of Continuous Model Theory
Boris Zilber
We recast the well-known axiom system of quantum mechanics used by physicists (the Dirac calculus) in the language of Continuous Logic. For the basic version of the axiomatic syste…
Structural approximation and a Minkowski space-time lattice with Lorentzian invariance
Boris Zilber
We introduce a framework of structural approximation to represent Lorentz-invariant Minkowski space-time as the limit of finite cyclic lattices, each equipped with the action of a…
Axioms of Quantum Mechanics in light of Continuous Model Theory
Boris Zilber
We revisit Dirac's axiomatization of quantum mechanics and show that it can essentially be reformulated in a more familiar logical setting - continuous model theory. Our aim is two…
On the logical structure of physics
Boris Zilber
One of the main claims of the paper is that Dirac's calculus and broader theories of physics can be treated as theories written in the language of Continuous Logic. Establishing it…