6:15 PM
Hi, I'm looking for someone familiar with the transfinite recursion theorem because I don't really understand what it's saying or what's its significance
3 hours later…
9:41 PM
And this theorem says that $G(\alpha)$ is uniquely defined, if you have some kind of assignment which gives unique object based on values of $G(\beta)$ for $\beta<\alpha$.
4
More formally, we can state the Transfinite Recursion Theorem as follows. Given a class function $G\colon V\to V$, there exists a unique transfinite sequence $F\colon\mathrm{Ord}\to V$ (where $\mathrm{Ord}$ is the class of all ordinals) such that $F(\alpha) = G(F\upharpoonright\alpha)$ for al...
4
I am trying to understand transfinite recursion. So far I have encountered two different definitions of this theorem (not completely sure whether they describe the same Principle of Transfinite Recursion). The first one: If I have a map $I:X^{<\alpha}\rightarrow X$ (for $\alpha$ some ordinal ...
10:36 PM
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