Weiss W.A.R. An Introduction to Set Theory

CreateSpace Independent Publishing Platform, 2014. — 157 p. — ISBN: 1502970597.Thoroughly revised, updated, expanded, and reorganized to serve as a primary text for mathematics courses, This book covers the basics: relations, functions, orderings, finite, countable, and uncountable sets, and cardinal and ordinal numbers. It gives students sufficient grounding in a rigorous approach to the revolutionary results of set theory as well as pleasure in being able to tackle significant problems that arise from the theory.
It also provides five additional self-contained chapters, consolidates the material on real numbers into a single updated chapter affording flexibility in course design, supplies end-of-section problems, with hints, of varying degrees of difficulty, includes new material on normal forms and Goodstein sequences, and adds important recent ideas including filters, ultrafilters, closed unbounded and stationary sets, and partitions.
The proofs in this textbook are rigorous, clear, and complete, while remaining accessible to undergraduates who are new to upper-level mathematics. Exercises are included at the end of each section in a chapter, with useful suggestions for the more challenging exercises.LOST
FOUND
The Axioms of Set Theory
The Natural Numbers
The Ordinal Numbers
Relations and Orderings
Cardinality
What's So Real About The Real Numbers?
Ultralters Are Useful
The Universe
Reection
Elementary Submodels
Constructibility
Appendices
The Axioms of ZFC
Tentative Axioms