This textbook supplies an advent to axiomatic set idea and examines the admired questions which are correct in present learn in a fashion that's available to scholars. Its major topic is the interaction of enormous cardinals, internal versions, forcing and descriptive set theory.

The following themes are covered:

• Forcing and constructability

• The Solovay-Shelah Theorem i.e. the equiconsistency of ‘every set of reals is Lebesgue measurable’ with one inaccessible cardinal

• advantageous constitution concept and a latest method of sharps

• Jensen’s overlaying Lemma

• The equivalence of analytic determinacy with sharps

• the idea of extenders and generation trees

• an evidence of projective determinacy from Woodin cardinals.

*Set Theory* calls for just a easy wisdom of mathematical good judgment and should be appropriate for complicated scholars and researchers.