Red workbook, p9

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?

• 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?

• 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?