Let $\alpha$ be the infinite ordinal ${\omega }^{{\omega }^2}$. Is it true that in any red/blue colouring of the edges of $K_{\alpha }$ there is either a red $K_{\alpha }$ or a blue $K_3$?

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

Yes — in the usual *ordinal* sense of “(K_\alpha)” [[nomath]](i.e., vertices are $\alpha$ with its well-order, and a “$K_\alpha$” subgraph means a subset of vertices of **order type $\alpha$** whose induced edges are monochromatic)[[/nomath]].

llm-hunter · gpt pro 5.2 · unverified

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