Questions tagged [ultrafinitism]

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How strong is exponentiation with only open induction? (Or: "how low can we go?")

Do the strongest theories currently known to be unconstrained by Tennenbaum's theorem ($IOpen$ and some modest extensions) remain so when augmented with a definition of exponentiation and axiom $\...
Robin Saunders's user avatar
4 votes
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What is the meaning and proof of Harvey Friedman’s ultrafinite incompleteness sentence?

On page 7 of his paper “Adventures in Incompleteness”, Harvey Friedman states the following: IN ANY LONG ENOUGH SEQUENCE $x_1,...,x_n$ FROM $\{1,2,3\}$, SOME $(x_i,...,x_{2i})$ IS A SUBSEQUENCE OF ...
Keshav Srinivasan's user avatar
4 votes
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The Return of Graham Arithmetics: adding induction up to $g_{64}$

In my previous question The inconsistency of Graham Arithmetics plus $ \forall n, n < g_{64}$, I introduced an extension of Robinson Arithmetics with the recursive definition of Tetraction, a small ...
Mirco A. Mannucci's user avatar