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 Goldblatt, Robert.
 Cambridge ; New York : Cambridge University Press, 2011.
 Description
 Book — xiii, 268 p. ; 24 cm.
 Summary

 Introduction and overview
 1. Logics with actualist quantifiers
 2. The Barcan formulas
 3. The existence predicate
 4. Propositional functions and predicate substitution
 5. Identity
 6. Cover semantics for relevant logic References Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data) 9781107010529 20160605
Science Library (Li and Ma)
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QA9.46 .G664 2011  Unknown 
 Goldblatt, Robert.
 New York : Springer, c1998.
 Description
 Book — xiv, 289 p. ; 24 cm.
 Summary

 What are the Hyperreals? Large Sets. Ultrapower Construction of the Hyperreals. The Transfer Principle. Hyperreals Great and Small. Convergence of Sequences and Series. Continuous Functions. Differentiation. The Riemann Integral. Topology of the Reals. Internal and External Sets. Internal Functions and Hyperfinite Sets. Universes and Frameworks. The Existence of Nonstandard Entities. Permanence, Comprehensiveness, Saturation. Loeb Measure. Ramsey Theory. Completion by Enlargement. Hyperfinite Approximation. Books on Nonstandard Analysis.
 (source: Nielsen Book Data)
(source: Nielsen Book Data) 9780387984643 20160528
 Online
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QA299.82 .G65 1998  Available 
3. Lectures on the Hyperreals [electronic resource] : an Introduction to Nonstandard Analysis [1998]
 Goldblatt, Robert.
 New York, NY : Springer New York, 1998.
 Description
 Book — 1 online resource (xiv, 293 pages).
 Summary

 I Foundations.
 1 What Are the Hyperreals?. 1.1 Infinitely Small and Large. 1.2 Historical Background. 1.3 What Is a Real Number?. 1.4 Historical References.
 2 Large Sets. 2.1 Infinitesimals as Variable Quantities. 2.2 Largeness. 2.3 Filters. 2.4 Examples of Filters. 2.5 Facts About Filters. 2.6 Zorn's Lemma. 2.7 Exercises on Filters.
 3 Ultrapower Construction of the Hyperreals. 3.1 The Ring of RealValued Sequences. 3.2 Equivalence Modulo an Ultrafilter. 3.3 Exercises on AlmostEverywhere Agreement. 3.4 A Suggestive Logical Notation. 3.5 Exercises on Statement Values. 3.6 The Ultrapower. 3.7 Including the Reals in the Hyperreals. 3.8 Infinitesimals and Unlimited Numbers. 3.9 Enlarging Sets. 3.10 Exercises on Enlargement. 3.11 Extending Functions. 3.12 Exercises on Extensions. 3.13 Partial Functions and Hypersequences. 3.14 Enlarging Relations. 3.15 Exercises on Enlarged Relations. 3.16 Is the Hyperreal System Unique?.
 4 The Transfer Principle. 4.1 Transforming Statements. 4.2 Relational Structures. 4.3 The Language of a Relational Structure. 4.4 *Transforms. 4.5 The Transfer Principle. 4.6 Justifying Transfer. 4.7 Extending Transfer.
 5 Hyperreals Great and Small. 5.1 (Un)limited, Infinitesimal, and Appreciable Numbers. 5.2 Arithmetic of Hyperreals. 5.3 On the Use of "Finite" and "Infinite". 5.4 Halos, Galaxies, and Real Comparisons. 5.5 Exercises on Halos and Galaxies. 5.6 Shadows. 5.7 Exercises on Infinite Closeness. 5.8 Shadows and Completeness. 5.9 Exercise on Dedekind Completeness. 5.10 The Hypernaturals. 5.11 Exercises on Hyperintegers and Primes. 5.12 On the Existence of Infinitely Many Primes. II Basic Analysis.
 6 Convergence of Sequences and Series. 6.1 Convergence. 6.2 Monotone Convergence. 6.3 Limits. 6.4 Boundedness and Divergence. 6.5 Cauchy Sequences. 6.6 Cluster Points. 6.7 Exercises on Limits and Cluster Points. 6.8 Limits Superior and Inferior. 6.9 Exercises on lim sup and lim inf. 6.10 Series. 6.11 Exercises on Convergence of Series.
 7 Continuous Functions. 7.1 Cauchy's Account of Continuity. 7.2 Continuity of the Sine Function. 7.3 Limits of Functions. 7.4 Exercises on Limits. 7.5 The Intermediate Value Theorem. 7.6 The Extreme Value Theorem. 7.7 Uniform Continuity. 7.8 Exercises on Uniform Continuity. 7.9 Contraction Mappings and Fixed Points. 7.10 A First Look at Permanence. 7.11 Exercises on Permanence of Functions. 7.12 Sequences of Functions. 7.13 Continuity of a Uniform Limit. 7.14 Continuity in the Extended Hypersequence. 7.15 Was Cauchy Right?.
 8 Differentiation. 8.1 The Derivative. 8.2 Increments and Differentials. 8.3 Rules for Derivatives. 8.4 Chain Rule. 8.5 Critical Point Theorem. 8.6 Inverse Function Theorem. 8.7 Partial Derivatives. 8.8 Exercises on Partial Derivatives. 8.9 Taylor Series. 8.10 Incremental Approximation by Taylor's Formula. 8.11 Extending the Incremental Equation. 8.12 Exercises on Increments and Derivatives.
 9 The Riemann Integral. 9.1 Riemann Sums. 9.2 The Integral as the Shadow of Riemann Sums. 9.3 Standard Properties of the Integral. 9.4 Differentiating the Area Function. 9.5 Exercise on Average Function Values.
 10 Topology of the Reals. 10.1 Interior, Closure, and Limit Points. 10.2 Open and Closed Sets. 10.3 Compactness. 10.4 Compactness and (Uniform) Continuity. 10.5 Topologies on the Hyperreals. III Internal and External Entities.
 11 Internal and External Sets. 11.1 Internal Sets. 11.2 Algebra of Internal Sets. 11.3 Internal Least Number Principle and Induction. 11.4 The Overflow Principle. 11.5 Internal OrderCompleteness. 11.6 External Sets. 11.7 Defining Internal Sets. 11.8 The Underflow Principle. 11.9 Internal Sets and Permanence. 11.10 Saturation of Internal Sets. 11.11 Saturation Creates Nonstandard Entities. 11.12 The Size of an Internal Set. 11.13 Closure of the Shadow of an Internal Set. 11.14 Interval Topology and HyperOpen Sets.
 12 Internal Functions and Hyperfinite Sets. 12.1 Internal Functions. 12.2 Exercises on Properties of Internal Functions. 12.3 Hyperfinite Sets. 12.4 Exercises on Hyperfiniteness. 12.5 Counting a Hyperfinite Set. 12.6 Hyperfinite Pigeonhole Principle. 12.7 Integrals as Hyperfinite Sums. IV Nonstandard Frameworks.
 13 Universes and Frameworks. 13.1 What Do We Need in the Mathematical World?. 13.2 Pairs Are Enough. 13.3 Actually, Sets Are Enough. 13.4 Strong Transitivity. 13.5 Universes. 13.6 Superstructures. 13.7 The Language of a Universe. 13.8 Nonstandard Frameworks. 13.9 Standard Entities. 13.10 Internal Entities. 13.11 Closure Properties of Internal Sets. 13.12 Transformed Power Sets. 13.13 Exercises on Internal Sets and Functions. 13.14 External Images Are External. 13.15 Internal Set Definition Principle. 13.16 Internal Function Definition Principle. 13.17 Hyperfiniteness. 13.18 Exercises on Hyperfinite Sets and Sizes. 13.19 Hyperfinite Summation. 13.20 Exercises on Hyperfinite Sums.
 14 The Existence of Nonstandard Entities. 14.1 Enlargements. 14.2 Concurrence and Hyperfinite Approximation. 14.3 Enlargements as Ultrapowers. 14.4 Exercises on the Ultrapower Construction.
 15 Permanence, Comprehensiveness, Saturation. 15.1 Permanence Principles. 15.2 Robinson's Sequential Lemma. 15.3 Uniformly Converging Sequences of Functions. 15.4 Comprehensiveness. 15.5 Saturation. V Applications.
 16 Loeb Measure. 16.1 Rings and Algebras. 16.2 Measures. 16.3 Outer Measures. 16.4 Lebesgue Measure. 16.5 Loeb Measures. 16.6 ?Approximability. 16.7 Loeb Measure as Approximability. 16.8 Lebesgue Measure via Loeb Measure.
 17 Ramsey Theory. 17.1 Colourings and Monochromatic Sets. 17.2 A Nonstandard Approach. 17.3 Proving Ramsey's Theorem. 17.4 The Finite Ramsey Theorem. 17.5 The ParisHarrington Version. 17.6 Reference.
 18 Completion by Enlargement. 18.1 Completing the Rationals. 18.2 Metric Space Completion. 18.3 Nonstandard Hulls. 18.4 padic Integers. 18.5 padic Numbers. 18.6 Power Series. 18.7 Hyperfinite Expansions in Base p. 18.8 Exercises.
 19 Hyperfinite Approximation. 19.1 Colourings and Graphs. 19.2 Boolean Algebras. 19.3 Atomic Algebras. 19.4 Hyperfinite Approximating Algebras. 19.5 Exercises on Generation of Algebras. 19.6 Connecting with the Stone Representation. 19.7 Exercises on Filters and Lattices. 19.8 HyperfiniteDimensional Vector Spaces. 19.9 Exercises on (Hyper) Real Subspaces. 19.10 The HahnBanach Theorem. 19.11 Exercises on (Hyper) Linear Functionals.
 20 Books on Nonstandard Analysis.
 (source: Nielsen Book Data)
(source: Nielsen Book Data) 9781461268413 20160614
Online 4. Mathematics of modality [1993]
 Goldblatt, Robert.
 Stanford, Calif. : CSLI Publications, c1993.
 Description
 Book — v, 273 p. : ill. ; 24 cm.
 Summary

 Introduction
 1. Metamathematics of modal logic
 2. Semantic analysis of orthologic
 3. Orthomodularity is not elementary
 4. Arithmetical necessity, provability and intuitionistic logic
 5. Diodorean modality in Minkowski spacetime
 6. Grothendieck topology as geometric modality
 7. The semantics of Hoare's iteration rule
 8. An abstract setting for Henkin proofs
 9. A framework for infinitary modal logic
 10. The McKinsey axiom is not canonical
 11. Elementary logics are canonical and pseudoequational Bibliography Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data) 9781881526247 20160528
 Also online at

Green Library, Philosophy Library (Tanner), Science Library (Li and Ma)
Green Library  Status 

Find it Stacks  
P51 .C18 NO.43  Unknown 
Philosophy Library (Tanner)  Status 

Stacks  
QA9.46 .G66 1993  Unknown 
Science Library (Li and Ma)  Status 

Stacks  
P51 .C18 NO.43  Unknown 
5. Logics of time and computation [1992]
 Goldblatt, Robert.
 2nd ed., rev. and expanded.  Stanford, CA : Center for the Study of Language and Information, c1992.
 Description
 Book — 180 p.
 Summary

 Preface to the first edition Preface to the second edition Part I. Propositional Modal Logic:
 1. Syntax and semantics
 2. Proof theory
 3. Canonical models and completeness
 4. Filtrations and decidability
 5. Multimodal languages
 6. Temporal logic
 7. Some topics in metatheory Part II. Some Temporal and Computational Logic:
 8. Logics with linear frames
 9. Temporal logic of concurrency
 10. Propositional dynamic logic Part III. FirstOrder Dynamic Logic:
 11. Assignments, substitutions, and quantifiers
 12. Syntax and semantics
 13. Proof theory
 14. Canonical model and completeness Bibliography Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data) 9780937073933 20160528
 Online
Green Library, Philosophy Library (Tanner), Science Library (Li and Ma)
Green Library  Status 

Find it Jonsson Social Sciences Reading Room: CSLI publications  
P51 .C18 NO.7  Inlibrary use 
Philosophy Library (Tanner)  Status 

Stacks  
QA9.46 .G65 1992  Unknown 
Science Library (Li and Ma)  Status 

Stacks  
P51 .C18 NO.7  Unknown 
Online 6. Logics of time and computation [1987]
 Goldblatt, Robert.
 Stanford, CA : Center for the Study of Language and Information, c1987.
 Description
 Book — ix, 131 p. ; 24 cm.
 Summary

 Preface to the first edition Preface to the second edition Part I. Propositional Modal Logic:
 1. Syntax and semantics
 2. Proof theory
 3. Canonical models and completeness
 4. Filtrations and decidability
 5. Multimodal languages
 6. Temporal logic
 7. Some topics in metatheory Part II. Some Temporal and Computational Logic:
 8. Logics with linear frames
 9. Temporal logic of concurrency
 10. Propositional dynamic logic Part III. FirstOrder Dynamic Logic:
 11. Assignments, substitutions, and quantifiers
 12. Syntax and semantics
 13. Proof theory
 14. Canonical model and completeness Bibliography Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data) 9780937073933 20160528
 Also online at

7. Orthogonality and spacetime geometry [1987]
 Goldblatt, Robert.
 New York : SpringerVerlag, c1987.
 Description
 Book — viii, 189 p. : ill. ; 24 cm.
SAL3 (offcampus storage)
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QA477 .G65 1987  Available 
8. Topoi, the categorial analysis of logic [1984]
 Goldblatt, Robert.
 Rev. ed.  Amsterdam ; New York ; NorthHolland ; New York, N.Y. : Sole distributors for the U.S.A. and Canada, Elsevier NorthHolland, 1984.
 Description
 Book — xvi, 551 p. : ill. ; 23 cm.
 Summary

 Mathematics = Set Theory? What Categories Are. Arrows Instead of Epsilon. Introducing Topoi. Topos Structure: First Steps. Logic Classically Conceived. Algebra of Subobjects. Intuitionism and its Logic. Functors. Set Concepts and Validity. Elementary Truth. Categorical Set Theory. Arithmetic. Local Truth. Adjointness and Quantifiers. Logical Geometry.
 (source: Nielsen Book Data)
(source: Nielsen Book Data) 9780444867117 20160528
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

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QA169 .G64 1983  Unknown 
 Goldblatt, Robert.
 Berlin ; New York : SpringerVerlag, 1982.
 Description
 Book — xi, 304 p. ; 24 cm.
 Online

 dx.doi.org SpringerLink
 Google Books (Full view)
SAL3 (offcampus storage)
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QA76.7 .G65 1982  Available 
QA76.7 .G65 1982  Available 
10. Topoi, the categorial analysis of logic [1979]
 Goldblatt, Robert.
 Amsterdam ; New York : NorthHolland Pub. Co. ; New York : sole distributors for the U.S.A. and Canada, Elsevier North Holland, 1979.
 Description
 Book — xv, 486 p. : ill. ; 23 cm.
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA169 .G64  Unknown 
 Goldblatt, Robert, RDPSA.
 1st ed.  Cape Town : Reijger, 1984.
 Description
 Book — 267 p., [4] p. of plates : ill. ; 26 cm.
 Online
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HE7351.Z7 C374 1984  Available 
 Downey, R. G. (Rod G.)
 Singapore : World Scientific Publishing Company, 2013.
 Description
 Book — 1 online resource (346 pages)
 Summary

 Preface; Contents; Resolute Sequences in Initial Segment Complexity G. Barmpalias and R.G. Downey;
 1. Introduction; 1.1. Formal expressions of resoluteness; 1.2. Resoluteness and complexity;
 2. Resoluteness and sparseness;
 3. Jump inversion with Kresolute sequences;
 4. Completely resolute and resolutefree degrees; Acknowledgments; References; Approximating Functions and Measuring Distance on a Graph W. Calvert, R. Miller and J. Chubb Reimann;
 1. Introduction;
 2. Reducibilities on Functions;
 3. Functions Approximable from Above;
 4. The Distance Function in Computable Graphs.
 5. Related TopicsAcknowledgments; References; Carnap and McKinsey: Topics in the PreHistory of PossibleWorl Semantics M.J. Cresswell;
 1. The `metalinguistic' approach to the logical modalities;
 2. Carnap validity;
 3. Quine/Carnap validity;
 4. Meaning postulates;
 5. Classes of models;
 6. McKinsey's `syntactical' interpretation;
 7. Restricted substitution functions; References; Limits to Joining with Generics and Randoms A.R. Day and D.D. Dzhafarov;
 1. Introduction;
 2. A nonjoining theorem for generics;
 3. Extensions to other forcing notions;
 4. A nonjoining theorem for randoms.
 AcknowledgementsReferences; Freedom & Consistency M. Detlefsen;
 1. Introduction;
 2. Freedom & Consistency;
 3. The Futility Argument;
 4. Premise 2;
 5. Premise 3;
 6. Conclusion; References; A van Lambalgen Theorem for Demuth Randomness D. Diamondstone, N. Greenberg and D. Turetsky;
 1. Introduction; 1.1. Partial relativization vs. full relativization; 1.2. Survey of van Lambalgen's theorem for various randomness notions; 1.3. Notation;
 2. A van Lambalgen theorem for Demuth randomness;
 3. Does a stronger version of van Lambalgen's theorem hold for Demuth randomness?; References.
 Faithful Representations of Polishable Ideals S. Gao1. Introduction;
 2. Faithful representations for abelian Polish groups;
 3. Faithful representations for Polishable ideals; Acknowledgment; References; Further Thoughts on Definability in the Urysohn Sphere I. Goldbring;
 1. Introduction;
 2. Finitely Definable Sets;
 3. Arbitrary Definable Sets;
 4. Special Definable Functions; References; Simple Completeness Proofs for Some Spatial Logics of the Real Line I. Hodkinson;
 1. Introduction;
 2. Definitions; 2.1. Syntax
 Lformulas; 2.2. Kripke semantics; 2.3. Linear orders; 2.4. Linear models.
 3. Construction of linear models3.1. Lexicographic sums; 3.2. Intervals of R; 3.3. Shuffles;
 4. The logic of R with;
 5. The logic of R with and;
 6. The logic of R with and;
 7. Conclusion; Acknowledgments; References; On a Question of Csima on ComputationTime Domination X. Hua, J. Liu and G. Wu;
 1. Introduction;
 2. Requirements and basic strategy;
 3. Construction;
 4. Verification; References; A Generalization of Beth Model to Functionals of High Types F. Kachapova;
 1. Introduction;
 2. Definitions; 2.1. Definition of Beth model; 2.2. Facts about Beth models.
(source: Nielsen Book Data) 9789814449267 20190129
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