# Questions tagged [transfinite-recursion]

Questions dealing with set-theoretic functions defined by transfinite recursion.

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### Defining a function using transfinite recursion.

For $p,q\in \mathbb{Q} :p<q$ we define $(p,q) :=\{ x\in \mathbb Q : p<x<q \}$ and we want to define an order like this $$(p,q) < (t,l) \iff p<q$$ and I want to prove that there is an ...
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### How does Reinhardt's extension of the set-theoretic universe beyond $V_\Omega$ work?

In this answer it is stated that in William Reinhardt's paper 'Remarks on reflection principles, large cardinals, and elementary embeddings' (1974) Reinhardt suggests extending the set-theoretic ...
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### Implementing L-Systems for conversion (instead of drawing): Extending the Hilbert space filling curve

I have been reading for some time about L-Systems, and specifically the Hilbert Space filling curve. I am interested in writing a function to convert upper-triangular matrix coordinates into an 1-...
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### A Proof of Transfinite Recursion Theorem

This proof takes me a huge amount of time to formulate, so I hope that someone can help me verify it. There're possibly subtle mistakes that I'm unable to recognize. Thank you for your dedicated help! ...
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### Strong induction with recursive definition function

Look at following recursive function definition for function $F :\mathbb{N}​\times\mathbb{N}​ \to \mathbb{N}$​: $$\begin{split} F(x,0) & = 0\\ F(x,n) & = x + F(x, n-1) \end{split}$$ Prove ...