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I'm doing my masters in Mathematics and took a class in universal algebra and there I learned that for example: Boolean algebras have direct connection with classical logic, Heyting algebras with intuitionistic logic.

I got fascinated by this connection of logic and algebra and self studied about the Lindembaum-Tarski method and nowdays I'm studying the link between the relational semantics of intuitionistic logic (Kripke semantics) and their algebraic one.

But all this is quite old and for beginners. So my question is:

What is going on on the field of algebraic logic those days? The field is full of research or not much populated anymore? What are the trends? If possible, I would love to see some reference where I can read and learn more about the state of the field these days.

Observation: I saw another post with the same question posted 7 years ago, but could not access the link in the answer of this post. Since the question was asked 7 years ago, I think I can ask the same question again? If no, please let me know and I will delete my question.

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    $\begingroup$ The next thing you should discover is categorical logic. $\endgroup$
    – Andrej Bauer
    Commented Jul 16, 2021 at 16:00
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    $\begingroup$ @VictorRafael Note that there are different types of infinitesimal calculus, not all of which need category theory. The earliest fully rigorous approach was nonstandard analysis, which uses model theory instead. $\endgroup$
    – Noah Schweber
    Commented Jul 16, 2021 at 16:32
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    $\begingroup$ @VictorRafael this Amazon link might be broken at some point, so it can be useful to provide some info: The continuous, the discrete and the infinitesimal in philosophy and mathematics, by John L. Bell. $\endgroup$
    – YCor
    Commented Jul 16, 2021 at 16:33
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    $\begingroup$ @VictorRafael: Mike Shulman has some notes on categorical logic and so do Steve Awodey and I. Ours are supposed to be unpublished but if you google for "Bauer Awodey Categorical logic" the will appear. Perhaps I should try to take those down and rely on the Streisand effect to get popular. $\endgroup$
    – Andrej Bauer
    Commented Jul 16, 2021 at 17:03
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    $\begingroup$ @AndrejBauer Awodey and Bauer's notes should be banned. They are scandalous, morally lax, and a dangerously corrupting influence on the young people of today. (Is that helping, Andrej?) $\endgroup$
    – Tom Leinster
    Commented Jul 24, 2021 at 15:40

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