06/06/2022, 07:37 PM
Just few words, I'll reply in details asap.
Yes, I was inspired by Andy's consecutive piecewise extensions method And I wanted to study the behavior of a couple of piece-wise extensions of goodstein. As of Hamkins' answer, it came in November, 4 months after my post here, and I was really excited at first when I red it.
This concept is still valid. On an abstract level, everything is controlled by that first strip, like a boundary condition. It is in fact a kind of boundary condition and I can prove that it comes from the decomposition \(\mathbb R\simeq \mathbb N\times [0,1)\). Interesting question is how to detect if the function on \(0\leq x <1\) comes from something that globally is analytic/smooth.
I'll add more.
Yes, I was inspired by Andy's consecutive piecewise extensions method And I wanted to study the behavior of a couple of piece-wise extensions of goodstein. As of Hamkins' answer, it came in November, 4 months after my post here, and I was really excited at first when I red it.
This concept is still valid. On an abstract level, everything is controlled by that first strip, like a boundary condition. It is in fact a kind of boundary condition and I can prove that it comes from the decomposition \(\mathbb R\simeq \mathbb N\times [0,1)\). Interesting question is how to detect if the function on \(0\leq x <1\) comes from something that globally is analytic/smooth.
I'll add more.
Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)
\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)