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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.
List of Papers Grouped by Subject Matter
Foreword on Terminology
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 Nα"
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 Apart
Algebraic Theories, Algebraic Categories, and Algebraic Functors
Extensive Ultraproducts and Haar Measure
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 Theory
Bibliography with Explanatory Notes
Some Notes on the Theory Of Models
A Bibliography of the Theory of Models
List of Registered Participants
- No. of pages:
- © North Holland 1963
- 1st January 1963
- North Holland
- eBook ISBN:
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