Shelah’s Model without P-points– part 7

My apologies for the blogging hiatus. Let’s continue.

Read more about this series at the first post.

Part 7: switching filters

In short:

  • From $u$ to $\{ \omega \} \otimes u$.

 

Page 7

Shelah's model without P-points page 7

 

Part 7 as PDF

Part 7 as Xournal-source

Shelah’s Model without P-points– part 4

Read more about this series at the first post.

Part 4: $\omega^\omega$-bounding

In short:

  • Basic Properties:
    • Grigorieff forcing and the Sacks variant are $\omega^\omega$-bounding

 

Page 4

Shelah's model without P-points page 4

 

Part 4 as PDF

Part 4 as Xournal-source

Shelah’s Model without P-points– part 3

Read more about this series at the first post.

Part 3: More Strategy and Shelah’s “crucial fact”

In short:

  • Basic Properties:
  • a strategy for $\omega^\omega$-bounding — continued.
  • The “crucial fact” for Grigorieff and Sacks forcing (that’s what Shelah calls it)
Page 3

Shelah's model without P-points page 3

 

Part 3 as PDF

Part 3 as Xournal-source

Shelah’s Model without P-points– part 1

To get some research back into this blog, I will, over the course of the next few weeks, post some handwritten notes about a couple of well-known results by Shelah: the model without P-points, the model with a unique selective ultrafilter and the model with a unique P-point.

These notes were written for my recent series of talks at the UofM’s Logic Seminar here in Ann Arbor and came out of an ongoing collaboration with David Chodounsky from Prague. The source for this presentation is Shelah’s Proper and Improper Forcing.

The notes were written using Xournal.

Part 1: Basic Definitions

In short:

  • Definitions
    • Grigorieff forcing
    • Sacks forcing with a filter
    • P-filter, P-point
    • non-meagre filter

 

Page 1

Page 1

Part 1as PDF

Part 1 as Xournal-source