03347nam 22004935 450 991090619670332120250807152921.09783031716607303171660410.1007/978-3-031-71660-7(CKB)36549437100041(MiAaPQ)EBC31776825(Au-PeEL)EBL31776825(DE-He213)978-3-031-71660-7(EXLCZ)993654943710004120241112d2024 u| 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierThe Forcing Method in Set Theory An Introduction via Boolean Valued Logic /by Matteo Viale1st ed. 2024.Cham :Springer Nature Switzerland :Imprint: Springer,2024.1 online resource (246 pages)La Matematica per il 3+2,2038-5757 ;1689783031716591 3031716590 - 1. Introduction -- 2. Preliminaries: Preorders, Topologies, Axiomatizations of Set Theory -- 3. Boolean Algebras -- 4. Complete Boolean Algebras -- 5. More on Preorders -- 6. Boolean Valued Models -- 7. Forcing.The main aim of this book is to provide a compact self-contained presentation of the forcing technique devised by Cohen to establish the independence of the continuum hypothesis from the axioms of set theory. The book follows the approach to the forcing technique via Boolean valued semantics independently introduced by Vopenka and Scott/Solovay; it develops out of notes I prepared for several master courses on this and related topics and aims to provide an alternative (and more compact) account of this topic with respect to the available classical textbooks. The aim of the book is to take up a reader with familiarity with logic and set theory at the level of an undergraduate course on both topics (e.g., familiar with most of the content of introductory books on first-order logic and set theory) and bring her/him to page with the use of the forcing method to produce independence (or undecidability results) in mathematics. Familiarity of the reader with general topology would also be quite helpful; however, the book provides a compact account of all the needed results on this matter. Furthermore, the book is organized in such a way that many of its parts can also be read by scholars with almost no familiarity with first-order logic and/or set theory. The book presents the forcing method outlining, in many situations, the intersections of set theory and logic with other mathematical domains. My hope is that this book can be appreciated by scholars in set theory and by readers with a mindset oriented towards areas of mathematics other than logic and a keen interest in the foundations of mathematics.La Matematica per il 3+2,2038-5757 ;168Logic, Symbolic and mathematicalMathematical Logic and FoundationsLogic, Symbolic and mathematical.Mathematical Logic and Foundations.511.3Viale Matteo324101MiAaPQMiAaPQMiAaPQBOOK9910906196703321The Forcing Method in Set Theory4290128UNINA