Set Theory: Boolean-Valued Models and Independence ProofsOUP Oxford, 5 mei 2011 - 216 pagina's This third edition, now available in paperback, is a follow up to the author's classic Boolean-Valued Models and Independence Proofs in Set Theory,. It provides an exposition of some of the most important results in set theory obtained in the 20th century: the independence of the continuum hypothesis and the axiom of choice. Aimed at graduate students and researchers in mathematics, mathematical logic, philosophy, and computer science, the third edition has been extensively updated with expanded introductory material, new chapters, and a new appendix on category theory. It covers recent developments in the field and contains numerous exercises, along with updated and increased coverage of the background material. This new paperback edition includes additional corrections and, for the first time, will make this landmark text accessible to students in logic and set theory. |
Inhoudsopgave
First Steps | |
Forcing and Some Independence Proofs | |
Problems | |
Group Actions on V B and the Independence of the Axiom of Choice | |
Generic Ultrafilters and Transitive Models of | |
Cardinal Collapsing Boolean Isomorphism and Applications to the Theory | |
Iterated Boolean Extensions Martins Axiom and Sousliirs Hypothesis | |
The relative consistency of | |
Booleanvalued Analysis | |
Intuitionistic Set Theory and HeytingAlgebraValued Models | |
Boolean and Heyting AlgebraValued Models as Categories | |
Historical Notes | |
Index of Symbols | |
Overige edities - Alles bekijken
Set Theory: Boolean-Valued Models and Independence Proofs John L. Bell Geen voorbeeld beschikbaar - 2005 |
Set Theory : Boolean-Valued Models and Independence Proofs: Boolean-Valued ... John L. Bell Geen voorbeeld beschikbaar - 2005 |
Veelvoorkomende woorden en zinsdelen
antichain arbitrary arrow f assertion assume automorphism axiom of choice B-valued bijection Boolean completion Boolean extension Boolean-valued models called canonical map commutes complete Boolean algebra complete Heyting algebra complete subalgebra construction continuum hypothesis Corollary countable define dense subset disjoint distributive lattice dom(p dom(u dom(v element equivalent extensional filter finite first-order following conditions follows immediately formula function Hence holds homomorphism implies infinite cardinal intuitionistic isomorphism Lemma Let G logic M-generic subset M-generic ultrafilter Maximum Principle model of ZFC nonempty object one-one ordinal partially ordered set partition of unity power set Problem Proof Let prove real numbers recursion relative consistency result S-complete sentence sequence Set H set theory Show that V(B Solovay Suppose supremum Theorem topology topos transitive model ultrafilter uncountable unique w₁ well-founded relation well-ordered whence ZF is consistent