In comments on Quora (see, for example, here, here, here), Ron Maimon has repeatedly expressed the strong opinion that Hilbert's program was not killed by Gödel's results in the way typically ...
Is there a proof of the consistency of Analysis (second order arithmetic), which is similar to Gentzen's proof of the consistency of arithmetic? Update: Which (different) methods can be used to ...
The theory of Diophantine equations is one of the main stream research areas in number theory. There are many known results and unknown conjectures about the existence of non-trivial solutions for ...
In Ordinal Analysis, Proof-theoretic Ordinal of a theory is thought as measure of a consistency strength and computational power. Is it always the case? I. e. are there some general results about ...
Let $\kappa$ be a cardinal (of uncountable cofinality). A subset $S \subseteq \kappa$ is called stationary if it intersects every club, i.e. closed unbounded subset of $\kappa$. Now my question is ...
Sometime around 1975, Leo Harrington wrote a set of notes, apparently 13 pages long, entitled Kolmogorov's $R$-operator and the first nonprojectible ordinal. I do not know how widely they were ...