Tag: pseudo-intersection number

Stevo’s Forcing Class Fall 2012 – Class 2

(This is the second lecture in Stevo Todorcevic’s Forcing class, held in the fall of 2012. You can find the first lecture here. Quotes by Stevo are in dark blue; some are deep, some are funny, some are paraphrased so use your judgement.)

(Also, there are bound to be typos. I would appreciate anyone who could point them out in the comments and I will promptly fix them.)

Summary

  • Give the classic example of a \sigma -centred poset. (The one that adds a “small” subset of \omega .)
  • Define the various “Martin numbers”: \mathfrak{m}, \mathfrak{m}_{SH} and \mathfrak{m}_{sep} .
  • Define some small cardinals \mathfrak{p}, \mathfrak{t} and \mathfrak{b} .
  • Show that \mathfrak{m} = \mathfrak{m}_{SH} and \mathfrak{m}_{sep} = \mathfrak{p} .

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