Introduction to and Historical Overview of Quantum Logics

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Introductory lecture summary:
1. Finite dimensional hilbert spaces and (complemented) modular lattices; infinite-dimensional hilbert spaces and orthomodularity.
2. von Neumann's QL; von Neumann-Birkhoff (briefly!); reconstruction of QM from P(H)
3. Mackey's programme; some early axiomatics (e.g., Zierler); QLs as OMPs + order-determining sets of states
4. Piron's Theorem; some discussion of Piron's axioms
5. Keller's examples (maybe just a mention, though I'd like to indicate how they come up); Soler's theorem (just the statement)
6. Abstract OMLs; Greechie Diagrams and the Loop Lemma; brief mention of Harding's results on decompositions
7. Tensor products (the F-R example, showing OMLs not stable under tensor products); orthoalgebras.
8. Orthoalgebras from test spaces