دانلود کتاب Advances in Mathematical Logic: Dedicated to the Memory of Professor Gaisi Takeuti, SAML 2018, Kobe, Japan, September 2018, Selected, Revised

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Preface Organization Contents Reflection Principles, Generic Large Cardinals, and the Continuum Problem 1 Gödel's Program and Large Cardinals 2 Reflection Principles 3 Game Reflection Principles and Generically Large Cardinals 4 Simultaneous Reflection down to <20 and leq20 5 Reflection Principles Under Large Continuum 6 Laver-Generic Large Cardinals 7 Some Open Problems and Takeuti's Account on Gödel's Contribution to the Continuum Problem References On Supercompactness of ω1 1 Introduction 2 Definitions and Basic Concepts 3 Choice Principles and Supercompactness of ω1 4 Chang Model and Supercompactness of ω1 5 Weak Homogeneity and Supercompactness of ω1 6 AD+, ADmathbbR, and Supercompactness of ω1 7 HPC and Supercompactness of ω1 References Interpolation Properties for Sacchetti's Logics 1 Introduction 2 Sacchetti's Logics wGLn 3 Sequent Calculi for Sacchetti's Logics 3.1 Kripke Semantics 3.2 Proof Search Procedure 3.3 Cut-Admissibility 4 Craig Interpolation Property for wGLn 5 Circular Proof System 6 Lyndon Interpolation Property for wGLn 7 Concluding Remarks References Rosser Provability and the Second Incompleteness Theorem 1 Introduction 2 Provability Predicates and Derivability Conditions 3 Rosser Provability Predicates 4 Main Theorems 4.1 Proof of Theorem 9 4.2 Proof of Theorem 10 4.3 Proof of Theorem 11 References On Takeuti's Early View of the Concept of Set 1 Introduction 2 An Overview of Takeuti's View of the Concept of Set 3 Themes in Takeuti's View of the Concept of Set 3.1 Critical Remarks on the Concept of Set 3.2 The Concept of Set to Be Analyzed by Finitistic Methods 4 Closing Remarks References On Countable Stationary Towers 1 Introduction 2 Results References Reforming Takeuti's Quantum Set Theory to Satisfy de Morgan's Laws 1 Introduction 2 Preliminaries 2.1 Quantum Logic 2.2 Commutators 2.3 Conditionals 3 Quantum Set Theory 4 Transfer Principle References Choiceless Löwenheim–Skolem Property and Uniform Definability of Grounds 1 Introduction 2 Preliminaries 3 Löwenheim–Skolem Cardinals 4 Uniform Definability of Grounds 5 The Mantle and the Generic Mantle 6 When AC is Forceable References Irrational-Based Computability of Functions 1 Introduction 2 Preliminaries 3 Irrational-Based Computable Function 4 Examples 5 Irrational-Based Effective Convergence of Function Sequence 6 Final Note: Classical Account References ``Gaisi Takeuti's Finitist Standpoint'' and Its Mathematical Embodiment 1 Introduction 2 ``Takeuti's'' Hilbert's Program 3 Takeuti's Finitist Standpoint 4 My View 5 Some Reflections on Takeuti's Thoughts 6 Framework of Consistency Proofs 6.1 Framework of Gentzen-Takeuti Consistency Proofs 6.2 Proof-Theoretic Order Structure 7 Accessibility Proofs 7.1 Takeuti's Attempt: Eliminators 7.2 Accessibility Proof of Ordinal Diagrams 7.3 System ASOD 8 Functional Interpretation 9 Universe of Mechanisms 10 Some Explanations 11 In Retrospect References Properness Under Closed Forcing 1 Introduction 2 The First Example 3 The Second Example References