Paul wrote: > About three days ago, I got stuck when reading a paper by the great combinatorist, Rado.
I hope you get the reply you're hoping for.
Meanwhile your title "Surprise at my failure to resolve an issue in an elementary paper by Rado" reminded me of my students days: I was surprised if I understood a journal paper. I failed to understand stuff in many a textbook. For example, I couldn't get past page 21 (I think it was) in Sacks's 'Saturated model theory'.
This paragraph may not mean anything to you, in which case skip to the next one. Sacks was defining S |= phi (S a structure, phi a formula). I knew of two definitions: Taski's and McKinsey's. I could see (without the need to understand) that Sack's method wasn't Tarski's. So I assumed that it was McKinsey's or a near relative. I worked backwards knowing that "S |= phi" meant "phi is true in S", and was able to understand what a map (called sigma by Sacks, I seem to recall) was doing. Sacks's explanation was utterly obscure (to me--I was, and I remain, thick) but by keeping McKinsey's definition in mind I came to understand what sigma was.
I think my experience described in the previous paragraph may be broadly relevant. If you know, from some other source, what Rado's Theorem 1 means (and maybe how to prove it, but, chiefly, what it means), can you work backwards from the conclusion that you know and understand and thus see what Rado is doing?