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I'm supposed to give a reference for Mathematical logic to a friend of mine. He is not a Mathematics student. He's read a little about sets and knows "$\land$", "$\lor$", and "$\lnot$", for example. He only wants to be familiar with it and taste it, to understand what a regular deduction in math means. So I think the reference can have topics like set theory, I mean including de-morgan laws and similar topics.

Which Mathematical logic book is suitable for one who likes Mathematics but is not Mathematics student?

Thank you.

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I liked Introdution to mathematical logic by Elliot Mendelson when I start in maths. You can even find the pdf in google.

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There are many branches of mathematical logic that are pretty different and would likely require different suggestions.

In terms of Model Theory, maybe Sider's Logic For Philosophy would be a good place to start. It's not by a mathematician but Model Theory is Model Theory. It's the intro model theory textbook used at UChicago for undergrads in philosophy. The one we use in math courses is not really suitable for someone without a background in mathematics.

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