Download PDF by Paul C. Eklof: Almost Free Modules: Set-Theoretic Methods

By Paul C. Eklof

ISBN-10: 0444885021

ISBN-13: 9780444885029

This can be a longer remedy of the set-theoretic concepts that have reworked the learn of abelian team and module thought during the last 15 years. a part of the ebook is new paintings which doesn't look somewhere else in any shape. moreover, a wide physique of fabric which has seemed formerly (in scattered and infrequently inaccessible magazine articles) has been commonly remodeled and in lots of instances given new and greater proofs. The set concept required is punctiliously built with algebraists in brain, and the independence effects are derived from explicitly acknowledged axioms. The publication comprises workouts and a consultant to the literature and is appropriate to be used in graduate classes or seminars, in addition to being of curiosity to researchers in algebra and common sense.

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Extra resources for Almost Free Modules: Set-Theoretic Methods

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12. Suppose K is a measurable cardinal. (i) For any subset X of K of cardinality K there is a K-complete ultrafilter on K which contains X . (ii) There is a subset S of P ( K )such that S has cardinality 2" and for every X # Y in S, IX n YI < K [cf. 51. (iii) There are 2" different 6-complete ultrafilters on K .

Filters and large cardinals Throughout this section I will denote an arbitrary (infinite) set. 1 Definition. A filter on I is a subset D of P ( I ) satisfying: (1) 8 $! D ,I E D ; ( 2 ) if X , Y E D,then X n Y E D; (3) if X E D and X 2 Y C I , then Y E D. If Y is a subset of I , the principal filter generated b y Y is the filter D E P ( I ) :Y C_ X I . If D is not equal to DY for any Y C_ I , D is called non-principal. An ultrafilter on I is a filter D on I such that for every X C I , either X E D or I\X E D.

I) if X E D and p o ( X ) = 0 if X $! D. , whenever {Xv: u < A } is a partition of Y and X < K , then po(Y) = Cu

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Almost Free Modules: Set-Theoretic Methods by Paul C. Eklof

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