## Hilbert Logic

**Authors:** J.A.J. van Leunen

Early in the twentieth century a suitable foundation of quantum physics was found in traditional quantum logic. This idea exploits the lattice isomorphism between the set of propositions of a quantum logic system and the set of closed subspaces of an infinite dimensional separable Hilbert space. Later Constantin Piron restricted the choice for the number systems that can be used for specifying the inner product of the Hilbert space to members of a division ring. A slight refinement of the quantum logic system extends the lattice isomorphism to a topological isomorphism. This new logic system will be called Hilbert logic and it has a striking resemblance with a separable Hilbert space. The paper also provides insight in how fields can be interpreted.

**Comments:** 6 Pages.

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### Submission history

[v1] 2013-02-22 07:40:19

[v2] 2013-03-04 16:20:04

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