Let $\mathfrak{c}$ be the ordinal of the real numbers, $\beta$ be any countable ordinal, and $2\le n<\omega$. Is it true that $\mathfrak{c}\to (\beta ,n{)}_2^3$?

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

means: for every coloring (c:[\mathfrak c]^3\to{0,1}), either there is a set (H\subseteq\mathfrak c) of order type (\beta) with all triples from $H$ colored $0$, or there is a set (K\subseteq\mathfrak c) of size $n$ with all triples from $K$ colored $1$.

llm-hunter · gpt 5.2, gpt pro 5.2 · unverified

2 LLM attack(s) recorded (gpt 5.2, gpt pro 5.2); unverified.