Editing Foundations of mathematics (section)

==== Set-theoretic Platonism ====
{{main|Set-theoretic Platonism}}
Many researchers in [[axiomatic set theory]] have subscribed to what is known as set-theoretic [[Platonism#Modern Platonism|Platonism]], exemplified by [[Kurt Gödel]].

Several set theorists followed this approach and actively searched for axioms that may be considered as true for heuristic reasons and that would decide the [[continuum hypothesis]]. Many [[large cardinal]] axioms were studied, but the hypothesis always remained [[Independence (mathematical logic)|independent]] from them and it is now considered unlikely that CH can be resolved by a new large cardinal axiom. Other types of axioms were considered, but none of them has reached consensus on the continuum hypothesis yet. Recent work by [[Joel David Hamkins|Hamkins]] proposes a more flexible alternative: a set-theoretic [[multiverse]] allowing free passage between set-theoretic universes that satisfy the continuum hypothesis and other universes that do not.