|dc.description.abstract||The infinite in mathematics has two manifestations. Its occurrence in analysis has been satisfactorily formalized and demystified by the δ method of Bolzano, Cauchy and Weierstrass. It is of course the 'set-Theoretic infinite' that concerns me here. Once the existence of an infinite set is accepted, the axioms of set theory imply the existence of a transfinite hierarchy of larger and larger orders of infinity. I shall review some well-known facts about the influence of these axioms of infinity to the everyday mathematical practice and point out to some, as of yet not understood, phenomena at the level of the third-order arithmetic. Technical details from both set theory and operator algebras are kept at the bare minimum. In the Appendix, I include definitions of arithmetical and analytical hierarchies in order to make this paper more accessible to non-logicians. In this paper I am taking a position intermediate between pluralism and non-pluralism (as defined by P. Koellner in the entry on large cardinals and determinacy of the Stanford Encyclopaedia of Philosophy) with an eye for applications outside of set theory.||en|
|dc.relation.ispartof||Lecture Notes Series, Institute for Mathematical Sciences||en|
|dc.title||Absoluteness, truth, and quotients||en|
checked on Dec 3, 2023
checked on Dec 1, 2023
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.