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Below is an image that I took of a symbol in "Logic for Philosophy" by Theodore Sider. The symbol is used to represent a function whose domain is Sentence letters of propositional logic and whose range is the set {0,1} (Called a PL-Interpretation... it basically assigns truth value to different capital letters). What is the name of this symbol and how can it be reproduced in LaTeX?

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You can use Detexify to answer such questions, for example:

Screenshot

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You should have a look at: How to look up a symbol or identify a math symbol or character?

Using Detexify you can see, that this symbol is called \mathscr{I} and you need to include \usepackage{ mathrsfs } to use it.

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And an alternative name is \mathcal{I} from the calrsfs package.

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