Tag: Baire-Class-1

Stevo’s Forcing Class Fall 2012 – Class 15

(This is the fifteenth lecture in Stevo Todorcevic’s Forcing class, held in the fall of 2012. You can find the fourteenth lecture here. Quotes by Stevo are in dark blue; some are deep, some are funny, some are paraphrased so use your judgement. As always I appreciate any type of feedback, including reporting typos, in the comments below.)

Summary

  • We introduce free sequences.
  • A lemma (2) relating free sequences and \pi -bases is proved.
  • We prove that the generic ultrafilter is countably generated.
  • We construct nice \sigma -disjoint \pi -bases.
  • A realted theorem about compact spaces supporting a radon measure is proved as a corollary.

Continue reading Stevo’s Forcing Class Fall 2012 – Class 15

Stevo’s Forcing Class Fall 2012 – Class 14

(This is the fourteenth lecture in Stevo Todorcevic’s Forcing class, held in the fall of 2012. You can find the thirteenth lecture here. Quotes by Stevo are in dark blue; some are deep, some are funny, some are paraphrased so use your judgement. As always I appreciate any type of feedback, including reporting typos, in the comments below.)

Summary

  • We spend the entire lecture proving a theorem about Baire-Class-1 functions.
  • The proof is interesting because it uses forcing.
  • The entire proof is in the inductive step.

Continue reading Stevo’s Forcing Class Fall 2012 – Class 14

Stevo’s Forcing Class Fall 2012 – Class 13

(This is the thirteenth lecture in Stevo Todorcevic’s Forcing class, held in the fall of 2012. You can find the twelfth lecture here. Quotes by Stevo are in dark blue; some are deep, some are funny, some are paraphrased so use your judgement. As always I appreciate any type of feedback, including reporting typos, in the comments below.)

Summary

  • We restate the strong lemma.
  • A handful of spaces are presented to illustrate the following theorem.
  • A theorem about Baire-Class-1 functions is stated. (Which is proved by forcing!)
  • The proof strategy is discussed.

Continue reading Stevo’s Forcing Class Fall 2012 – Class 13