elementary submodel

@downwardsLST

Math undergrad. Interested in just about anything, but in particular set theory. My own tweets are in English only, but I frequently answer in Portuguese.

Vrijeme pridruživanja: veljača 2019.

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  1. Do you think set theorists are logicians?

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  2. 6. velj

    And no, "that's because 7 is the first integer that's greater or equal to 1 plus two times the ceiling of its square root" is not a proof of the statement, it's only the reason why the number is not arbitrary and it shows up in the proof.

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  3. 6. velj

    Ok take a look at this nice s e v e n over here But seriously, that's because 7 is the first integer that's greater or equal to 1 plus two times the ceiling of its square root.

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  4. 31. sij

    A classic example of something that is provable in ZF but not in PA is the strengthened finite Ramsey theorem, a combinatorial principle. The fact above is the Paris-Harrington theorem and, of course, here goes its page on Wikipedia:

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  5. 31. sij

    First order PA (Peano axioms) is the same thing as ZFfin (ZF but instead of the axiom of infinity, we have its negation). This is the sense that there are invertible functions mapping formulas from one language to another that "preserve truth".

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  6. proslijedio/la je Tweet
    30. sij

    Well, that's embarrassing...

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  7. 29. sij

    I wanted to make a tweet like "one of these is not a forcing" but the only neat name I recall for that is "amoeba forcing". Please reply if you know any funny forcing names, specially if they give something cool.

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  8. proslijedio/la je Tweet
    27. sij

    ANNOUNCEMENT: I have founded the Journal of Mathematical Superiority. The editorial board is all Fields-medalists. Since we all know that a low acceptance rate is a sign that a journal is GOOD, JMS will be REJECTING ALL SUBMISSIONS, making it the best journal of all.

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  9. proslijedio/la je Tweet
    20. sij

    Is there a subset of the plane that is connected, but upon the removal of a (specific) point it becomes totally disconnected (any two points can be separated by a disjoint opens)? Of course, it should contain more than a single point. What does your intuition say?

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  10. proslijedio/la je Tweet

    Since this thread is going to make for depressing reading, I would like to counter it with the opposite experience. Namely, mine. 1/

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  11. proslijedio/la je Tweet
    18. sij

    If you take any real number and repeatedly applying the cosine to it, the result always converges to the same constant (0.73908...). This problem shows that the convergence is fast enough that the differences add up to some differentiable function.

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  12. 18. sij

    Never have I been to a Mathematics event where the people were half as well dressed as these guys. Is being casual in conferences a brazilian thing?

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  13. 16. sij
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  14. 11. sij

    I have just hit 200 followers and I said there would be a reveal. As I've also sheaved my beard, it might as well be a face reveal Oops, shaved*

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  15. 7. sij

    A little health tip for your battery: - Do not keep your phone plugged in when it reaches 100%, so avoid charging overnight. - Actually, letting the battery reach 0% and fully charging it is not good. - Reduce your phone usage when it's charging. Source:

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  16. 6. sij

    The ultraproduct satisfies a sentence if a big amount of models satisfy it (if the set of models that satisfies it belongs to the ultrafilter) The construction, well, I may write about it some other time. (10/10)

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  17. 6. sij

    But we do! We call them ultraproducts: we start with a set of models K and an ultrafilter over it. Then, we build the ultraproduct of the models from K over the ultrafilter. Satisfaction in the ultraproduct will be as follows: (9/10)

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  18. 6. sij

    So now we have an ultrafilter over T. For each sentence of T, there's an element of the ultrafilter that contains it. If we had a way to build a model such that its satisfaction is defined by "a big number of subsets of T has this formula in it", we would prove compactness!(8/10)

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  19. 6. sij

    Any family with the finite intersection property may be extended to an ultrafilter: Given a set X, an ultrafilter over X is a collection of "big" subsets from X. Every subset that is not big is small, and the complement of a small subset is big (and vice-versa) (7/10)

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  20. 6. sij

    That's because the intersection between PHI and PSI (phi and psi are sentences from T) is actually the set "PHI AND PSI", because a model for "phi and psi" satisfies both "phi" and "psi". This is called the "finite intersection property" (6/10)

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