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Math Help - What is important to say about a boolean algebra (or any other semantic)

  1. #1
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    What is important to say about a boolean algebra (or any other semantic)

    In this very moment, I have to discuss the semantics of a particular logic. The semantics consists of a particular case of boolean algebra. I have less than 24 hours to elaborate a paper on this subject. I have to do the best I can. However, I am not able to establish a table of content. I have to mention that it is a requirement thar the paper to be of high scientific and academic value (I do not mind this because there will be no sanction if I do not do it; I just gave my word to a few insisting professors).

    So, any idea or hint about the structure and content (table of content) of the work will be appreciated.
    Also, suggestions of interesting properties of some specific cases of boolean algebras are welcome, so I can check against my case.

    Also, this particular boolean algebra belongs to a specific class of boolean algebras. What should I mention about this specific class.

    P.S.: the boolean algebras are defined on finite, totally ordeerd sets; my intuition is that it could be extended for infinite, totally ordered sets; if I am right does it exist a general form of transfinite induction or, at least, an example that could help me?

    P.P.S.: the first encounter with my professors will be tomorrow, so I should come up with something decent, but the final version is allowed to be ready by friday noon.
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  2. #2
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    Re: What is important to say about a boolean algebra (or any other semantic)

    What is important to say about a boolean algebra (or any other semantic)
    Important properties include, of course, soundness and completeness, as well as finite model property: if a formula is false in some interpretation, then it is false a finite interpretation.

    the boolean algebras are defined on finite, totally ordeerd sets; my intuition is that it could be extended for infinite, totally ordered sets
    A Boolean algebra is a partially ordered set. One can build a so-called interval algebra from a totally ordered sets. Yes, Boolean algebras can be infinite.

    Also, this particular boolean algebra belongs to a specific class of boolean algebras. What should I mention about this specific class.
    Which class?

    Some types and properties of Boolean algebras as mentioned in Wikipedia and the Stanford Encyclopedia of Philosophy.
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