Realism, nonstandard set theory, and large cardinals

摘要: Abstract Mathematicians justify axioms of set theory “intrinsically”, by reference to the universe sets their intuition, and “extrinsically”, for example, considerations simplicity or usefullness mathematical practice. Here we apply same kind justifications Nonstandard Analysis argue acceptance BNST + (Basic Set Theory plus additional Idealization axioms). has nontrivial consequences standard theory; it implies existence inner models with measurable cardinals. We also consider how practice in , compare other existing nonstandard theories.