Peter Krautzberger on the web

Red workbook, p9


red workbook, p9
Red Workbook, p.9


  • “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?


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 $p$?