CUMC math presentation - need help!

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I have an undergrad math conference in Vancouver in July and I need to prepare a 25 or 50 minute speech to present at the conference. The audience is going to be mostly 3rd and 4th year students.

I want to present and develop the hyperreals using the compactness theorem, but I'm thinking this might be too much. I can't assume that these people have taken logic, so the compactness theorem requires an explanation of satisfiability, which in turn requires an explanation of models. If I brush over all that, then the construction will seem like I'm just pulling [censored] out of my ass.

Is this presentation doable? Is there some approach you guys could suggest? Or should I just pick a simpler topic?