CUMC math presentation - need help!

[2218]

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?

[thylacine]

What are the hyperreals?
FWIW I understand the rest of that paragraph.

[2218]

[ QUOTE ]
What are the hyperreals?
FWIW I understand the rest of that paragraph.

[/ QUOTE ]

A field containing R as a subset (but no non-real complex numbers). It also contains infinite numbers (i.e. E b A r s.t. r is real and b>r, where E and A are the quantifiers) and their inverses, the infinitesimals.

[blah_blah]

fwiw i am one of the organizers of said conference

i don't know much about logic but it's not really a big deal to give a talk on something very advanced. I think that you should try to avoid getting too wrapped up in details though; 25 minutes is enough to give heuristic proofs and talk about the importance/implications of various results, but rigorous proofs eat up a lot of time that you may or may not have.

[2218]

[ QUOTE ]
fwiw i am one of the organizers of said conference

i don't know much about logic but it's not really a big deal to give a talk on something very advanced. I think that you should try to avoid getting too wrapped up in details though; 25 minutes is enough to give heuristic proofs and talk about the importance/implications of various results, but rigorous proofs eat up a lot of time that you may or may not have.

[/ QUOTE ]

I didn't plan on giving rigorours proofs. I learned this stuff two months into a logic class, and even then it was a lot to swallow. So to just jump straight into it seems like it will be a challenge.

I really wanted to show the compactness theorem because it is a beautiful one, and its use here is just ingenious. I doubt that is practical, however, for reasons mentioned in my OP.

I'm thinking of just mentioning the compactness theorem (not even stating it) as the underlying foundation and then saying something like: "'everything' true in R is true in *R (hyperreals) with the added fact that *R has an element, b, simultaneously satisfying the following (infinite set of) sentences {x>1, x>2, x>3, ...}," and then proceding with the construction.

Thoughts?

[PairTheBoard]

I think you need to decide whether you want your talk to be about Symbolic Logic and Model Theory or about the HyperReals. I don't think you will have time to give a full treatment of both. I don't think you can assume people know much about Symbolic Logic and Model Theory. In two stints of Graduate Studies in mathematics, 3 and 4 years, I was never exposed to the subject. Once you get the HyperReals you should be able to show some interesting things you can do with them. Do they really make things easier?

PairTheBoard