In set theory "equiconsistency" (and not "consistency") of the theories is the main part of researches. So we usually try to construct a new model using a given one. In the ...
In some sense the empty set ($\emptyset$) and the global set of all sets ($G$) are the ends of the universe of mathematical objects. The world which $ZFC$ describes has an end from the bottom and is ...
Mathematician Edward Nelson is known for his extreme views on the foundations of mathematics, variously described as "ultrafintism" or "strict finitism" (Nelson's preferred term), which came into the ...
One of the most interesting novelties in recent foundational studies is Voevodsky's Homotopical Type Theory project (see here). Finally homotopy theory ideas have entered in a royal fashion the ...
(originally posted at MSE as Same same but different: Coextensive relations in model and set theory, slightly modified) The official definition of a structure in model theory in its presumably most ...
First of all, I am not an expert in model theory. I just want to get my personal view on the foundations of mathematics straight. I just learned in Sergey Melikhov's answer to another question ...
Most mathematicians seem to be contented with the fact, that abstract structures cannot be directly modelled as such in a set theory without ur-elements. What seems to me the standard stance: Set ...