Ultraproduct for Quantum Structures

Morteza Moniri, Elahe Shirinkalam

DOI: http://dx.doi.org/10.12775/LLP.2018.005


Quantum Kripke frames are certain quantum structures recently introduced by Zhong. He has defined certain properties such as Existence of Approximation and Superposition for these structures. In this paper, we define the ultraproduct for the family of quantum Kripke frames and show that the aforementioned properties are invariant under ultraproduct. In this way we prove that the ultraproduct of each family of quantum Kripke frames is also a quantum Kripke frame. We also show the same results for other related quantum structures.


Quantum Kripke frame; state space; ultraproduct

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