How would you explain one of these theorems in the foundations of mathematics to a fellow colleague outside the field of logic (or rather to an undergraduate mathematics student) handwaving over the ...
Recall that a certain type of object admits an ADE classification if there is a notion of equivalence relative to which equivalence classes of objects of the given type can be placed in one-to-one ...
Every student of set theory knows that the early axiomatization of the theory had to deal with spectacular paradoxes such as Russel's, Burali-Forti's etc. This is why the (self-contradictory) ...
Usually we have axiomatic theory and the we look for model for it - this is book picture. Of course in real math usual one has a "model" that is given structure and looks for proper axiomatizing of ...
Is there a sensible classification of the properties of structures with a given signature $\sigma$, e.g. graphs with $\sigma = \lbrace R \rbrace$? For example like this: properties defined by ...
Edit: Let me summarize what this question was meant to ask. Is there a quantitative theory of "approximate" soundness? Arguments are usually either sound or unsound. This is binary. If we don't ...