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Summary Proponents of decoherence-based interpretations of quantum mechanics aim to solve the measurement problem by appeal to the physical process of decoherence, without committing themselves to the full ontology of the many-worlds interpretation. 
Key works The theory of decoherent histories was developed independently by Robert Griffiths and by Murray Gell-Mann and James Hartle. Roland Omnes further developed and formalized Griffiths' approach. The best places to start are Gell-Mann and Hartle's original article (Gell-Mann & Hartle 1990), and the books by Griffiths (Griffiths 2002) and Omnes (Omnes 1999).
Introductions Griffiths 1999
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  1. Valia Allori, Detlef Duerr, Nino Zanghi & Sheldon Goldstein (2002). Seven Steps Toward the Classical World. Journal of Optics B 4:482–488.
    Classical physics is about real objects, like apples falling from trees, whose motion is governed by Newtonian laws. In standard quantum mechanics only the wave function or the results of measurements exist, and to answer the question of how the classical world can be part of the quantum world is a rather formidable task. However, this is not the case for Bohmian mechanics, which, like classical mechanics, is a theory about real objects. In Bohmian terms, the problem of the classical (...)
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  2. Guido Bacciagaluppi, The Role of Decoherence in Quantum Mechanics. Stanford Encyclopedia of Philosophy.
    Interference phenomena are a well-known and crucial feature of quantum mechanics, the two-slit experiment providing a standard example. There are situations, however, in which interference effects are (artificially or spontaneously) suppressed. We shall need to make precise what this means, but the theory of decoherence is the study of (spontaneous) interactions between a system and its environment that lead to such suppression of interference. This study includes detailed modelling of system-environment interactions, derivation of equations (‘master equations’) for the (reduced) state (...)
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  3. Guido Bacciagaluppi (2002). Remarks on Space-Time and Locality in Everett's Interpretation. In. In T. Placek & J. Butterfield (eds.), Non-Locality and Modality. Kluwer. 105--122.
  4. Carlos Alexandre Brasil, L. A. De Castro & R. D. J. Napolitano (2013). How Much Time Does a Measurement Take? Foundations of Physics 43 (5):642-655.
    We consider the problem of measurement using the Lindblad equation, which allows the introduction of time in the interaction between the measured system and the measurement apparatus. We use analytic results, valid for weak system-environment coupling, obtained for a two-level system in contact with a measurer (Markovian interaction) and a thermal bath (non-Markovian interaction), where the measured observable may or may not commute with the system-environment interaction. Analysing the behavior of the coherence, which tends to a value asymptotically close to (...)
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  5. Andrew Elby (1994). The 'Decoherence' Approach to the Measurement Problem in Quantum Mechanics. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1994:355 - 365.
    Decoherence results from the dissipative interaction between a quantum system and its environment. As the system and environment become entangled, the reduced density operator describing the system "decoheres" into a mixture (with the interference terms damped out). This formal result prompts some to exclaim that the measurement problem is solved. I will scrutinize this claim by examining how modal and relative-state interpretations can use decoherence. Although decoherence cannot rescue these interpretations from general metaphysical difficulties, decoherence may help these interpretations to (...)
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  6. Michael Epperson (2009). Quantum Mechanics and Relational Realism. Process Studies 38 (2):340-367.
    By the relational realist interpretation of wave function collapse, the quantum mechanical actualization of potentia is defined as a decoherence-driven process by which each actualization (in “orthodox” terms, each measurement outcome) is conditioned both by physical and logical relations with the actualities conventionally demarked as “environmental” or external to that particular outcome. But by the relational realist interpretation, the actualization-in-process is understood as internally related to these “enironmental” data per the formalism of quantum decoherence. The concept of “actualization via wave (...)
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  7. Chris Fields (2014). On the Ollivier–Poulin–Zurek Definition of Objectivity. Axiomathes 24 (1):137-156.
    The Ollivier–Poulin–Zurek definition of objectivity provides a philosophical basis for the environment as witness formulation of decoherence theory and hence for quantum Darwinism. It is shown that no account of the reference of the key terms in this definition can be given that does not render the definition inapplicable within quantum theory. It is argued that this is not the fault of the language used, but of the assumption that the laws of physics are independent of Hilbert-space decomposition. All evidence (...)
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  8. Alan Forrester (2007). Decision Theory and Information Propagation in Quantum Physics. Studies in History and Philosophy of Science Part B 38 (4):815-831.
    In recent papers, Zurek [(2005). Probabilities from entanglement, Born's rule pk=|ψk|2 from entanglement. Physical Review A, 71, 052105] has objected to the decision-theoretic approach of Deutsch [(1999) Quantum theory of probability and decisions. Proceedings of the Royal Society of London A, 455, 3129–3137] and Wallace [(2003). Everettian rationality: defending Deutsch's approach to probability in the Everett interpretation. Studies in History and Philosophy of Modern Physics, 34, 415–438] to deriving the Born rule for quantum probabilities on the grounds that it courts (...)
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  9. Irene Giardina & Alberto Rimini (1996). On the Existence of Inequivalent Quasideterministic Domains. Foundations of Physics 26 (8):973-987.
    In the framework of the history approach to quantum mechanics and, in particular, of the formulation of Gell-Mann and Hartle, the question of the existence of inequivalent decoherent sets of histories is reconsidered. A simple but acceptably realistic model of the dynamics of the universe is proposed and a particular set of histories is shown to be decoherent. By suitable tranformations of this set, a family of sets of histories is then generated, such that the sets, first, are decoherent on (...)
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  10. Amit Hagar, Does Protective Measurement Tell Us Anything About Quantum Reality?
    An analysis of the two routes through which one may disentangle a quantum system from a measuring apparatus, hence protect the state vector of a single quantum system from being disturbed by the measurement, reveals several loopholes in the argument from protective measurement to the reality of the state vector of a single quantum system.
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  11. Amit Hagar (2012). Decoherence: The View From the History and the Philosophy of Science. Phil. Trans. Royal Soc. London A 375 (1975).
    We present a brief history of decoherence, from its roots in the foundations of classical statistical mechanics, to the current spin bath models in condensed matter physics. We analyze the philosophical import of the subject matter in three different foundational problems, and find that, contrary to the received view, decoherence is less instrumental to their solutions than it is commonly believed. What makes decoherence more philosophically interesting, we argue, are the methodological issues it draws attention to, and the question of (...)
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  12. Amit Hagar (2012). Veiled Realism? Review of B d'Espagnat's On Physics and Philosophy. [REVIEW] Physics in Perspective (x).
  13. Robin Hanson (2003). When Worlds Collide: Quantum Probability From Observer Selection? [REVIEW] Foundations of Physics 33 (7):1129-1150.
    In Everett's many worlds interpretation, quantum measurements are considered to be decoherence events. If so, then inexact decoherence may allow large worlds to mangle the memory of observers in small worlds, creating a cutoff in observable world size. Smaller world are mangled and so not observed. If this cutoff is much closer to the median measure size than to the median world size, the distribution of outcomes seen in unmangled worlds follows the Born rule. Thus deviations from exact decoherence can (...)
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  14. Osvaldo Pessoa Jr (1997). Can the Decoherence Approach Help to Solve the Measurement Problem? Synthese 113 (3):323 - 346.
    This work examines whether the environmentally-induced decoherence approach in quantum mechanics brings us any closer to solving the measurement problem, and whether it contributes to the elimination of subjectivism in quantum theory. A distinction is made between 'collapse' and 'decoherence', so that an explanation for decoherence does not imply an explanation for collapse. After an overview of the measurement problem and of the open-systems paradigm, we argue that taking a partial trace is equivalent to applying the projection postulate. A criticism (...)
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  15. Olimpia Lombardi, Sebastian Fortin, Mario Castagnino & Juan Sebastián Ardenghi (2011). Compatibility Between Environment-Induced Decoherence and the Modal-Hamiltonian Interpretation of Quantum Mechanics. Philosophy of Science 78 (5):1024-1036.
    Given the impressive success of environment-induced decoherence (EID), nowadays no interpretation of quantum mechanics can ignore its results. The modal-Hamiltonian interpretation (MHI) has proved to be effective for solving several interpretative problems but, since its actualization rule applies to closed systems, it seems to stand at odds of EID. The purpose of this paper is to show that this is not the case: the states einselected by the interaction with the environment according to EID (the elements of the “pointer basis”) (...)
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  16. Edward MacKinnon, The Consistent Histories Interpretation of Quantum Mechanics.
    The consistent histories reformulation of quantum mechanics was developed by Robert Griffiths, given a formal logical systematization by Roland Omn\`{e}s, and under the label `decoherent histories', was independently developed by Murray Gell-Mann and James Hartle and extended to quantum cosmology. Criticisms of CH involve issues of meaning, truth, objectivity, and coherence, a mixture of philosophy and physics. We will briefly consider the original formulation of CH and some basic objections. The reply to these objections, like the objections themselves, involves a (...)
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  17. R. Omnes (2003). Consistent Quantum Theory - Robert B. Griffiths, Cambridge, 2001, Pp. 400, US $95, ISBN 0521803497. Studies in History and Philosophy of Science Part B 34 (2):329-331.
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  18. Roland Omnès (2011). Decoherence and Wave Function Collapse. Foundations of Physics 41 (12):1857-1880.
    The possibility of consistency between the basic quantum principles of quantum mechanics and wave function collapse is reexamined. A specific interpretation of environment is proposed for this aim and is applied to decoherence. When the organization of a measuring apparatus is taken into account, this approach leads also to an interpretation of wave function collapse, which would result in principle from the same interactions with environment as decoherence. This proposal is shown consistent with the non-separable character of quantum mechanics.
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