What is Meant by V?: Reflections on the Universe of All SetsThat the structure V = UaVa be the universe of all sets, that the set theoretical axioms be true assertions about V or that a question like the Continuum Hypothesis be still open (since it is undecided whether it holds or fails in V) are common assertions in set theory. How one is to understand them, tough, is not an obvious matter. The aim of this book is just to interpret the façon de parler that V is the universe of all sets in a way that is faithful to what is actually done in set theory. |
Common terms and phrases
2-logic a-priori appealing Axiom of Choice axioms of infinity Boolean broadest possible point Cantor chapter characterized claim concept of set consistency construction Continuum Hypothesis core models countable cumulative hierarchy defined different universes elementary embedding epistemic attitudes existence extrinsic fact final universe finite forcing extension forcing models forcing universes formulated framework for definitive Gödel Hauser heuristic higher set theory hold ideal inaccessible cardinals infinite inner model inner/core models interpreted intrinsic evidence introduced intuitions Jensen Kanamori Kunen large cardinal axioms large cardinal hypotheses logic Mahlo Martin mathematicians maximum iterative concept measurable cardinal model for ZFC notion obtained ordinal plausibility point of view practice of set principle proved question regard sense set theoretical achievements set theoretical axioms set theoretical universe Shelah Solovay stages structure Sy Friedman theorists tion transfinite true universes with different view on sets Wang Woodin cardinals Zermelo ZFC axioms