# Red workbook, p9

13 Mar 2014### Source

### Transcript

- “How far does a p-point travel?”
- $\rightarrow$ Flaskova: p-Pkt ⋅ p-Pkt kein p-Pkt
- $\curvearrowright$ Wegen der Eigenschaft p-Pkt muesste nicht $p+q$ in der Naehe von $p$ bleiben?
- $\rightarrow$ wenn ja, wie ist die Bahn einese p-Pkt?

- $\rightarrow$ Flaskova: p-Pkt ⋅ p-Pkt kein p-Pkt

- non-standards PA
- $\rightarrow$ als DS??

### partial Translation

- “How far does a p-point travel?”
- $\rightarrow$ Flašková: p-point ⋅ p-point (the product of two p-points) is not a p-point.
- $\curvearrowright$ Due to the properties of a p-point, shouldn’t $p+p$ somehow be “close” to $p$?
- $\rightarrow$ if so, what is the orbit of a p-point?

- $\rightarrow$ Flašková: p-point ⋅ p-point (the product of two p-points) is not a p-point.

- Can non-standard [models of] PA $\rightarrow$ [be considered] as dynamical system?

### Notes

Finally, a first note that is not some lecture note but (almost) a note on research. Not that it’s particularly meaningful or even sensible. In fact, it’s rather mysterious to me. At first I thought the background lies at TOPOSYM (which I visited during the summer), where Jana Flašková talked about P-points. But looking back at my notes on her talk (in the red workbook but not published here), I don’t think this really fits (but I might be wrong).

### Open Problems

- What can we say about $p+p$ for a P-point $P$?
- What can we say about (the closure of) subsemigroup generated by $p$?