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020 _a9783031716607
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024 7 _a10.1007/978-3-031-71660-7
_2doi
050 4 _aQA8.9-10.3
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072 7 _aPBC
_2thema
100 1 _aViale, Matteo.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_987370
245 1 4 _aThe Forcing Method in Set Theory
_h[electronic resource] :
_bAn Introduction via Boolean Valued Logic /
_cby Matteo Viale.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXIII, 242 p. 2 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLa Matematica per il 3+2,
_x2038-5757 ;
_v168
505 0 _a- 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.
520 _aThe 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.
650 0 _aMathematical logic.
_966195
650 1 4 _aMathematical Logic and Foundations.
_966198
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031716591
776 0 8 _iPrinted edition:
_z9783031716614
830 0 _aLa Matematica per il 3+2,
_x2038-5757 ;
_v168
_970145
856 4 0 _uhttps://doi.org/10.1007/978-3-031-71660-7
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
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