Set TheoryThis is a classic introduction to set theory in three parts. The first part gives a general introduction to set theory, suitable for undergraduates; complete proofs are given and no background in logic is required. Exercises are included, and the more difficult ones are supplied with hints. An appendix to the first part gives a more formal foundation to axiomatic set theory, supplementing the intuitive introduction given in the first part. The final part gives an introduction to modern tools of combinatorial set theory. This part contains enough material for a graduate course of one or two semesters. The subjects discussed include stationary sets, delta systems, partition relations, set mappings, measurable and real-valued measurable cardinals. Two sections give an introduction to modern results on exponentiation of singular cardinals, and certain deeper aspects of the topics are developed in advanced problems. |
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A₁ according to Theorem arbitrary ordinal Assume assumption Axiom of Choice axiom system called cf(A cf(k cofinal contradiction Corollary countable denoted disjoint sets elements equivalent Erdős filter formula free with respect function f Hence holds homogeneous in color infinite cardinal initial segment K-complete Lemma Let F limit ordinal mathematical measurable cardinal nonempty nonnegative integers normal ideal notation NS(K one-to-one operation order type ordered set pairwise disjoint sets partially ordered partition prime ideal proof of Theorem prove real numbers regressive function regular cardinal relation respect to f result Section sequence set mapping set system set theory Stat(K stationary sets stipulating strongly inaccessible cardinal subset successor ordinal symbol Theorem A7.1 transfinite induction transfinite recursion transitive ultrafilter w₁ weakly compact wellordered wellordered set Wff(L ΜΕΓ
References to this book
Set Theory: The Hajnal Conference, October 15-17, 1999, DIMACS Center Simon Thomas Limited preview - 2002 |