He's not comparing Frequentism and Bayesianism.
Not directly, no. But you would be hard-pressed to call Kolmogorov a Bayesian, at least when discussing axiomatic probability theory and not complexity/minimum description length, given that he never talked about "the degree of belief", only about axioms of probability. Yet his results match those of Jaynes (the other way around, really).
Further discussion on Kolmogorov and Bayes is in this paper posted on Luke's old blog. For example:
For an agent to be perfectly rational, her degrees of belief must obey the axioms of probability theory.
Question in title.
This is obviously subjective, but I figure there ought to be some "go-to" paper. Maybe I've even seen it once, but can't find it now and I don't know if there's anything better.
Links to multiple papers with different focus would be welcome. For my current purpose I have a preference for one that aims low and isn't too long.