The Theory of Models
Proceedings of the 1963 International Symposium at Berkeley
Published on 27. May 2014
510 pages
978-1-4832-7534-5 (ISBN)
Description
Studies in Logic and the Foundations of Mathematics: The Theory of Models covers the proceedings of the International Symposium on the Theory of Models, held at the University of California, Berkeley on June 25 to July 11, 1963. The book focuses on works devoted to the foundations of mathematics, generally known as "the theory of models." The selection first discusses the method of alternating chains, semantic construction of Lewis's systems S4 and S5, and continuous model theory. Concerns include ordered model theory, 2-valued model theory, semantics, sequents, axiomatization, formulas, axiomatic approach to hierarchies, alternating chains, and difference hierarchies. The text also ponders on Boolean notions extended to higher dimensions, elementary theories with models without automorphisms, and applications of the notions of forcing and generic sets. The manuscript takes a look at a hypothesis concerning the extension of finite relations and its verification for certain special cases, theories of functors and models, model-theoretic methods in the study of elementary logic, and extensions of relational structures. The text also reviews relatively categorical and normal theories, algebraic theories, categories, and functors, denumerable models of theories with extra predicates, and non-standard models for fragments of number theory. The selection is highly recommended for mathematicians and researchers interested in the theory of models.
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Content
DedicationPrefaceList of Papers Grouped by Subject MatterForeword on TerminologyInvited Papers The Method of Alternating Chains Semantic Construction of Lewis'S Systems S4 and S5 Continuous Model Theory Independence Results in Set Theory Boolean Notions Extended to Higher Dimensions Elementary Theories with Models without Automorphisms Combinatorial Theorems for the Construction of Models Some Applications of the Notions of Forcing and Generic Sets (Summary) A Hypothesis Concerning the Extension of Finite Relations and its Verification for Certain Special Cases. First Part The Theories of Functors and Models Languages with Added Quantifier "There Exist at Least Na" Model-Theoretic Methods in the Study of Elementary Logic Extensions of Relational Structures Finite Approximations of Infinitely Long Formulas Topics in the Theory of Definition Logical Structures Arising in Quantum Theory Model-Theoretic Invariants: Applications to Recursive and Hyperarithmetic Operations Semantical Analysis of Modal Logic II. Non-Normal Modal Propositional Calculi The Fraenkel-Mostowski Method for Independence Proofs in Set Theory Free Product in General Algebras Model-Theoretic Methods and Results in the Theory of Cylindric Algebras Reductions of Higher-Order Logic Omitting Classes of Elements Universal Groups of Automorphisms of Models Topics in Non-Archimedean Mathematics The Decision Problem for Fields On Models of Elementary Elliptic Geometry Logic with Denumerably Long Formulas and Finite Strings of Quantifiers Non-Standard Models for Fragments of Number Theory Applications of Model Theory to Degrees of Unsolvability Logics Appropriate to Empirical Theories On the Denumerable Models of Theories with Extra Predicates A Löwenheim-Skolem Theorem for Cardinals Far ApartContributed Papers Synonymous Theories Finite-Quantifier Equivalence Algebraic Theories, Algebraic Categories, and Algebraic Functors Extensive Ultraproducts and Haar MeasureAbstracts Relatively Categorical and Normal Theories Free Structures and Categories Finite-Dimensional Analogues to Boolean Algebras Boolean Recursive Functions and Closure Algebra A Unifying Principle in Quantification Theory 2No can be Anything it Ought to be Construction of a Model For Gödel-Bernays Set Theory for which the Class of Natural Numbers is a Set of the Model and a Proper Class in the TheoryBibliography with Explanatory Notes Some Notes on the Theory Of Models A Bibliography of the Theory of ModelsList of Registered Participants
