{"product_id":"constructivism-in-mathematics-vol-2-hardback-9780444703583","title":"Constructivism in Mathematics, Vol 2 (Hardback) 9780444703583","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eConstructivism in Mathematics, Vol 2\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eA.S. Troelstra (Author), D. van Dalen (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780444703583, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 1 November 1988\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e140 pages\u003cbr\u003e23.3 x 15.6 x 1.7 cm, 1.14 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\u003ci\u003eStudies in Logic and the Foundations of Mathematics, Volume 123: Constructivism in Mathematics: An Introduction, Vol. II\u003c\/i\u003e focuses on various studies in mathematics and logic, including metric spaces, polynomial rings, and Heyting algebras.\u003c\/p\u003e  \u003cp\u003eThe publication first takes a look at the topology of metric spaces, algebra, and finite-type arithmetic and theories of operators. Discussions focus on intuitionistic finite-type arithmetic, theories of operators and classes, rings and modules, linear algebra, polynomial rings, fields and local rings, complete separable metric spaces, and located sets. The text then examines proof theory of intuitionistic logic, theory of types and constructive set theory, and choice sequences.\u003c\/p\u003e  \u003cp\u003eThe book elaborates on semantical completeness, sheaves, sites, and higher-order logic, and applications of sheaf models. Topics include a derived rule of local continuity, axiom of countable choice, forcing over sites, sheaf models for higher-order logic, and complete Heyting algebras.\u003c\/p\u003e  \u003cp\u003eThe publication is a valuable reference for mathematicians and researchers interested in mathematics and logic. \u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eConstructivism in Mathematics: Contents Preliminaries\u003cbr\u003e7. The Topology of Metric Spaces\u003cbr\u003e     1. Basic Definitions\u003cbr\u003e     2. Complete, Separable Metric Spaces\u003cbr\u003e     3. Located Sets\u003cbr\u003e     4. Complete, Totally Bounded Spaces\u003cbr\u003e     5. Locally Compact Spaces\u003cbr\u003e     6. Notes\u003cbr\u003e     Exercises\u003cbr\u003e8. Algebra\u003cbr\u003e     1. Identity, Apartness and Order\u003cbr\u003e     2. Groups\u003cbr\u003e     3. Rings and Modules\u003cbr\u003e     4. Linear Algebra\u003cbr\u003e     5. Polynomial Rings\u003cbr\u003e     6. Fields and Local Rings\u003cbr\u003e     7. The Fundamental Theorem of Algebra\u003cbr\u003e     8. Notes\u003cbr\u003e     Exercises\u003cbr\u003e9. Finite-Type Arithmetic and Theories of Operators\u003cbr\u003e     1. Intuitionistic Finite-Type Arithmetic\u003cbr\u003e     2. Normalization, and a Term Model For HA?\u003cbr\u003e     3. The Theory APP\u003cbr\u003e     4. Models for APP\u003cbr\u003e     5. Abstract Realizability in APP\u003cbr\u003e     6. Extensionality and Choice in APP and HA?\u003cbr\u003e     7. Some Metamathematical Applications\u003cbr\u003e     8. Theories of Operators and Classes\u003cbr\u003e     9. Notes\u003cbr\u003e     Exercises\u003cbr\u003e10. Proof Theory of Intuitionistic Logic\u003cbr\u003e     1. Preliminaries\u003cbr\u003e     2. Normalization\u003cbr\u003e     3. The Structure of Normal Derivations of N-IQCE\u003cbr\u003e     4. The Decidability of IPC\u003cbr\u003e     5. Other Applications of Normalization\u003cbr\u003e     6. Conservative Addition of Predicative Classes\u003cbr\u003e     7. Sequent Calculi\u003cbr\u003e     8. N-IQC as a Calculus of Terms\u003cbr\u003e     9. Notes\u003cbr\u003e     Exercises\u003cbr\u003e11. The Theory of Types and Constructive Set Theory\u003cbr\u003e     1. Towards a Theory of Types\u003cbr\u003e     2. The Theory MLi0\u003cbr\u003e     3. Some Alternative Formulations of MLi0\u003cbr\u003e     4. The Types Nk and Reformulation of the E-Rules\u003cbr\u003e     5. The Theory ML0\u003cbr\u003e     6. Embeddings into APP\u003cbr\u003e     7. Extensions of MLi0 and ML0\u003cbr\u003e     8. Constructive Set Theory\u003cbr\u003e     9. Notes\u003cbr\u003e     Exercises\u003cbr\u003e12. Choice Sequences\u003cbr\u003e     1. Introduction\u003cbr\u003e     2. Lawless Sequences\u003cbr\u003e     3. The Elimination Translation for the Theory LS\u003cbr\u003e     4. Other Notions of Choice Sequence\u003cbr\u003e     5. Notes\u003cbr\u003e     Exercises\u003cbr\u003e13. Semantical Completeness\u003cbr\u003e     1. Beth Models\u003cbr\u003e     2. Completeness for Intuitionistic Validity\u003cbr\u003e     3. Incompleteness Results\u003cbr\u003e     4. Lattices, Heyting Algebras and Complete Heyting Algebras\u003cbr\u003e     5. Algebraic Semantics for IPC\u003cbr\u003e     6. O-Sets and Structures\u003cbr\u003e     7. Validity as Forcing\u003cbr\u003e     8. Postscript on Realizability\u003cbr\u003e     9. Notes\u003cbr\u003e     Exercises\u003cbr\u003e14. Sheaves, Sites and Higher-Order Logic\u003cbr\u003e     1. Presheaves, Sheaves and Sheaf-Completion\u003cbr\u003e     2. O-Presheaf and O-Sheaf Structures\u003cbr\u003e     3. Some Notions from Category Theory\u003cbr\u003e     4. Forcing Over Sites\u003cbr\u003e     5. Sheaf Models for Higher-Order Logic\u003cbr\u003e     6. Notes\u003cbr\u003e     Exercises\u003cbr\u003e15. Applications of Sheaf Models\u003cbr\u003e     1. Interpretation of N, Q, Z, R,N in Sh(O(T))\u003cbr\u003e     2. The Axiom of Countable Choice\u003cbr\u003e     3. Topologies in Sheaves Over a cHa\u003cbr\u003e     4. A Derived Rule of Local Continuity\u003cbr\u003e     5. The Monoid Model for CS\u003cbr\u003e     6. A Site Model for LS\u003cbr\u003e     7. Notes\u003cbr\u003e     Exercises\u003cbr\u003e16. Epilogue\u003cbr\u003e     1. The Role of Language and \"Informal Rigour\"\u003cbr\u003e     2. Intuitionistic Logic, Formalisms, and Equality\u003cbr\u003e     3. Brouwer's Theory of the Creative Subject\u003cbr\u003e     4. Dummett's Anti-Realist Argument\u003cbr\u003eBibliography\u003cbr\u003eIndex\u003cbr\u003eIndex of Names\u003cbr\u003eList of Symbols\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Elsevier Science","offers":[{"title":"Default Title","offer_id":46648500814104,"sku":"9780444703583","price":45.79,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780444703583_a8318b46-c9b9-4dd8-b0d6-11396ff6abcb.jpg?v=1694987417","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/constructivism-in-mathematics-vol-2-hardback-9780444703583","provider":"Freshly Printed Books","version":"1.0","type":"link"}