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Next
 Incurvati, Luca, author.
 New York : Cambridge University Press, 2019
 Description
 Book — 1 online resource
 Summary

 1. Concepts and conceptions
 2. The iterative conception
 3. Challenges to the iterative conception
 4. The naive conception
 5. The limitation of size conception
 6. The stratified conception
 7. The graph conception.
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(source: Nielsen Book Data)
 Incurvati, Luca, author.
 New York : Cambridge University Press, 2019
 Description
 Book — 1 online resource
 Summary

 1. Concepts and conceptions
 2. The iterative conception
 3. Challenges to the iterative conception
 4. The naive conception
 5. The limitation of size conception
 6. The stratified conception
 7. The graph conception.
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 Abrusci, V. M. (V. Michele), author.
 Milano, Italia : Springer, 2018.
 Description
 Book — 1 online resource (xiii, 439 pages)
 Summary

 1 Introduzione alla Parte I
 2 Decidibilità e risultati fondamentali di teoria della ricorsività
 3 L'aritmetica di Peano
 4 Introduzione alla Parte II
 5 La teoria assiomatica di Zermelo (Z) e quella di ZermeloFraenkel (ZF)
 6 Gli ordinali
 7 La gerarchia V e l'assioma di Fondazione
 8 L'assioma di scelta
 9 I cardinali.
5. Sets, functions, measures [2018]
 Zakharov, Valeriy K., author.
 Berlin : De Gruyter, [2018]
 Description
 Book — 2 volumes ; 25 cm.
 Summary

 Volume I. Fundamentals of set and number theory / Valeriy K. Zakharov, Timofey V. Rodionov
 Volume 2. Fundamentals of functions and measure theory / Valeriy K. Zakharov, Timofey V. Rodionov, Alexander V. Mikhalev.
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This comprehensive twovolume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff's classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for references to other sources. Along the lines of Hausdorff's initial work (1st ed., 1914), measure and integration theory is also included here as the third fundamental part of contemporary mathematics.The material about sets and numbers is placed in Volume 1 and the material about functions and measures is placed in Volume 2. Contents Fundamentals of the theory of classes, sets, and numbers Characterization of all natural models of Neumann  Bernays  Godel and Zermelo  Fraenkel set theories Local theory of sets as a foundation for category theory and its connection with the Zermelo  Fraenkel set theory Compactness theorem for generalized secondorder language.
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6. Intuitionistic set theory [2014]
 Bell, J. L. (John Lane)
 [London] : [King's] College Publications, c2014.
 Description
 Book — 120 p. ; 24 cm.
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

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QA248 .B445 2014  Unknown 
7. The logic of infinity [2014]
 Sheppard, Barnaby.
 Cambridge, U.K. : Cambridge University Press, 2014.
 Description
 Book — xxiv, 473 p. : ill. ; 25 cm
 Summary

 Preface
 Synopsis
 1. Introduction
 2. Logical foundations
 3. Avoiding Russell's paradox
 4. Further axioms
 5. Relations and order
 6. Ordinal numbers and the axiom of infinity
 7. Infinite arithmetic
 8. Cardinal numbers
 9. The axiom of choice and the continuum hypothesis
 10. Models
 11. From Godel to Cohen
 Appendix A. Peano arithmetic
 Appendix B. ZermeloFraenkel set theory
 Appendix C. Godel's incompleteness theorems
 Bibliography
 Index.
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Science Library (Li and Ma)
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Stacks  
QA248 .S54 2014  CHECKEDOUT Request 
 Hinkis, Arie.
 Heidelberg ; New York : Birkhäuser, c2013.
 Description
 Book — 1 online resource (426 p.)
 Summary

 Preface.  Part I: Cantor and Dedekind. Cantor's CBT proof for sets of the power of (II). Generalizing Cantor's CBT proof. CBT in Cantor's 1878 Beitrag. The theory of inconsistent sets. Comparability in Cantor's writings. The scheme of complete disjunction. Ruptures in the CantorDedekind correspondence. The inconsistency of Dedekind's infinite set. Dedekind's proof of CBT. Part II: The early proofs. Schroeder's Proof of CBT. Bernstein, Borel and CBT. Schoenflies' 1900 proof of CBT. Zermelo's 1901 proof of CBT. Bernstein's Division Theorem. Part III: Under the logicist sky. Russell's 1902 proof of CBT. The role of CBT in Russell's Paradox. Jourdain's 1904 generalization of Grundlagen. Harward 1905 on Jourdain 1904. Poincare and CBT. Peano's proof of CBT. J. Konig's strings gestalt. From kings to graphs. Jourdain's improvements round. Zermelo's 1908 proof of CBT. Korselt's proof of CB. Proofs of CBT in Principia Mathematica. The origin of Hausdorff Paradox in BDT. Part IV: At the Polish school. Sierpinski's proofs of BDT. Banach's proof of CBT. Kuratowski's proof of BDT. Early fixedpoint CBT proofs: Whittaker
 TarskiKnaster. CBT and BDT for ordertypes. Sikorski's proof of CBT for Boolean algebras. Tarski's proofs of BDT and the inequalityBDT. Tarski's FixedPoint Theorem and CBT. Reichbach's proof of CBT. Part V: Other ends and beginnings. Hellmann's proof of CBT. CBT and intuitionism. CBT in category theory. Conclusion. Bibliography. Index of names. Index of subjects.
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9. The structure of the real line [2011]
 Bukovský, Lev.
 Basel [Switzerland] : Birkhäuser, c2011.
 Description
 Book — xiv, 536 p. : ill. ; 24 cm.
 Summary

 Preface. 1 Introduction. 2 The Real Line. 3 Topology of Euclidean Spaces. 4 Measure Theory. 5 Useful Tools and Technologies. 6 Descriptive Set Theory. 7 Decline and Fall of the Duality. 8 Special Sets of Reals. 9 Additional Axioms. 10 Undecidable Statements. 11 Appendix. Bibliography. Index of Notation. Index.
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Science Library (Li and Ma)
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Stacks  
QA248 .B89 2011  Unknown 
10. Handbook of set theory [2010]
 Dordrecht : Springer, ©2010.
 Description
 Book — 1 online resource (xiv, 2197 pages) Digital: text file.PDF.
 Summary

 Handbook of Set Theory, Volume I, Akihiro Kanamori,
 0. Introduction Thomas Jech,
 1. Stationary Sets Andras Hajnal and Jean Larson,
 2. Partition Relations Stevo Todorcevic,
 3. Coherent Sequences Greg Hjorth,
 4. Borel Equivalence Relations Uri Abraham,
 5. Proper Forcing Andreas Blass,
 6. Combinatorial Cardinal Characteristics of the Continuum Tomek Bartoszynski,
 7. Invariants of Measure and Category Sy Friedman,
 8. Constructibility and Class Forcing 48 RalfDieter Schindler and Martin Zeman,
 9. Fine Structure 52 Philip Welch,
 10. S* Fine Structure 80 Volume II, Patrick Dehornoy,
 11. Elementary Embeddings and Algebra James Cummings,
 12. Iterated Forcing and Elementary Embeddings Matthew Foreman,
 13. Ideals and Generic Elementary Embeddings Uri Abraham and Menachem Magidor,
 14. Cardinal Arithmetic Todd Eisworth,
 15. Successors of Singular Cardinals Moti Gitik,
 16. PrikryType Forcings Volume III, William Mitchell,
 17. Beginning Inner Model Theory William Mitchell,
 18. The Covering Lemma John Steel,
 19. An Outline of Inner Model Theory Ernest Schimmerling,
 20. A Core Model Tool Box and Guide Steve Jackson,
 21. Structural Consequences of AD Itay Neeman,
 22. Determinacy in L(R) Peter Koellner and Hugh Woodin,
 23. Large Cardinals from Determinacy Paul Larson,
 24. Forcing over Models of Determinacy.
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 Lolli, Gabriele.
 Milan : Springer, 2008.
 Description
 Book — ix, 148 p. : ill.
12. The size of maximal almost disjoint families [2006]
 Monk, J. Donald (James Donald), 1930
 Warszawa : Institute of Mathematics, Polish Academy of Sciences, 2006.
 Description
 Book — 47 p. ; 24 cm.
 Online
SAL3 (offcampus storage)
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QA1 .D54 V.437  Available 
13. Théorie des ensembles [electronic resource] [2006]
 Bourbaki, Nicolas.
 Berlin : Springer, c2006.
 Description
 Book — 1 v. (various pagings) : ill.
 AMS Special Session Nonstandard Models of Arithmetic and Set Theory (2003 : Baltimore, Md.)
 Providence, R.I. : American Mathematical Society, c2004.
 Description
 Book — xii, 167 p. : ill. ; 26 cm.
 Summary

 Nonstandard models in a broader perspective by H. Gaifman Coding in $I\Delta_0$ by P. D'Aquino and J. F. Knight Automorphisms, Mahlo cardinals, and NFU by A. Enayat AC fails in the natural analogues of V and L that model the stratified fragment of ZF by T. Forster Working with nonstandard models by H. M. Friedman Internally iterated ultrapowers by K. Hrbacek On some questions of Hrbacek and Di Nasso by R. Jin Turing upper bounds of jump ideals and Scott sets by A. M. McAllister Diversity in substructures by J. H. Schmerl Automorphisms of countable recursively saturated models of set theory by A. A. Togha.
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QA248 .A634 2003  Available 
15. Theory of sets [1968]
 Théorie des ensembles. English
 Bourbaki, Nicolas.
 Berlin ; New York : Springer, [2004]
 Description
 Book — 1 online resource (viii, 414 pages) Digital: text file.PDF.
 Summary

 I. Description of Formal Mathematics. 1. Terms and relations. 1. Signs and assemblies. 2. Criteria of substitution. 3. Formative constructions. 4. Formative criteria. 2. Theorems. 1. The axioms. 2. Proofs. 3. Substitutions in a theory. 4. Comparison of theories. 3. Logical theories. 1. Axioms. 2. First consequences. 3. Methods of proof. 4. Conjunction. 5. Equivalence. 4. Quantified theories. 1. Definition of quantifiers. 2. Axioms of quantified theories. 3. Properties of quantifiers. 4. Typical quantifiers. 5. Equalitarian theories. 1. The axioms. 2. Properties of equality. 3. Functional relations. Appendix. Characterization of terms and relations. 1. Signs and words. 2. Significant words. 3. Characterization of significant words. 4. Application to assemblies in a mathematical theory. Exercises for 1. Exercises for 2. Exercises for 3. Exercises for 4. Exercises for 5. Exercises for the Appendix. II. Theory of Sets. 1. Collectivizing relations. 1. The theory of sets. 2. Inclusion. 3. The axiom of extent. 4. Collectivizing relations. 5. The axiom of the set of two elements. 6. The scheme of selection and union. 7. Complement of a set. The empty set. 2. Ordered pairs. 1. The axiom of the ordered pair. 2. Product of two sets. 3. Correspondences. 1. Graphs and correspondences. 2. Inverse of a correspondence. 3. Composition of two correspondences. 4. Functions. 5. Restrictions and extensions of functions. 6. Definition of a function by means of a term. 7. Composition of two functions. Inverse function. 8. Retractions and sections. 9. Functions of two arguments. 4. Union and intersection of a family of sets. 1. Definition of the union and the intersection of a family of sets. 2. Properties of union and intersection. 3. Images of a union and an intersection. 4. Complements of unions and intersections. 5. Union and intersection of two sets. 6. Coverings. 7. Partitions. 8. Sum of a family of sets. 5. Product of a family of sets. 1. The axiom of the set of subsets. 2. Set of mappings of one set into another. 3. Definitions of the product of a family of sets. 4. Partial products. 5. Associativity of products of sets. 6. Distributivity formulae. 7. Extension of mappings to products. 6. Equivalence relations. 1. Definition of an equivalence relation. 2. Equivalence classes
 quotient set. 3. Relations compatible with an equivalence relation. 4. Saturated subsets. 5. Mappings compatible with equivalence relations. 6. Inverse image of an equivalence relation
 induced equivalence relation. 7. Quotients of equivalence relations. 8. Product of two equivalence relations. 9. Classes of equivalent objects. Exercises for 1. Exercises for 2. Exercises for 3. Exercises for 4. Exercises for 5. Exercises for 6. III. Ordered Sets, Cardinals, Integers. 1. Order relations. Ordered sets. 1. Definition of an order relation. 2. Preorder relations. 3. Notation and terminology. 4. Ordered subsets. Product of ordered sets. 5. Increasing mappings. 6. Maximal and minimal elements. 7. Greatest element and least element. 8. Upper and lower bounds. 9. Least upper bound and greatest lower bound. 10. Directed sets. 11. Lattices. 12. Totally ordered sets. 13. Intervals. 2. Wellordered sets. 1. Segments of a wellordered set. 2. The principle of transfinite induction. 3. Zermelo's theorem. 4. Inductive sets. 5. Isomorphisms of wellordered sets. 6. Lexicographic products. 3. Equipotent sets. Cardinals. 1. The cardinal of a set. 2. Order relation between cardinals. 3. Operations on cardinals. 4. Properties of the cardinals 0 and 1. 5. Exponentiation of cardinals. 6. Order relation and operations on cardinals. 4. Natural integers. Finite sets. 1. Definition of integers. 2. Inequalities between integers. 3. The principle of induction. 4. Finite subsets of ordered sets. 5. Properties of finite character. 5. Properties of integers. 1. Operations on integers and finite sets. 2. Strict inequalities between integers. 3. Intervals in sets of integers. 4. Finite sequences. 5. Characteristic functions of sets. 6. Euclidean division. 7. Expansion to base b. 8. Combinatorial analysis. 6. Infinite sets. 1. The set of natural integers. 2. Definition of mappings by induction. 3. Properties of infinite cardinals. 4. Countable sets. 5. Stationary sequences. 7. Inverse limits and direct limits. 1. Inverse limits. 2. Inverse systems of mappings. 3. Double inverse limit. 4. Conditions for an inverse limit to be nonempty. 5. Direct limits. 6. Direct systems of mappings. 7. Double direct limit. Product of direct limits. Exercises for 1. Exercises for 2. Exercises for 3. Exercises for 4. Exercises for 5. Exercises for 6. Exercises for 7. Historical Note on 5. IV. Structures. 1. Structures and isomorphisms. 1. Echelons. 2. Canonical extensions of mappings. 3. Transportable relations. 4. Species of structures. 5. Isomorphisms and transport of structures. 6. Deduction of structures. 7. Equivalent species of structures. 2. Morphisms and derived structures. 1. Morphisms. 2. Finer structures. 3. Initial structures. 4. Examples of initial structures. 5. Final structures. 6. Examples of final structures. 3. Universal mappings. 1. Universal sets and mappings. 2. Existence of universal mappings. 3. Examples of universal mappings. Exercises for 1. Exercises for 2. Exercises for 3. Historical Note on Chapters IIV. Summary of Results. 1. Elements and subsets of a set. 2. Functions. 3. Products of sets. 4. Union, intersection, product of a family of sets. 5. Equivalence relations and quotient sets. 6. Ordered sets. 7. Powers. Countable sets. 8. Scales of sets. Structures. Index of notation. Index of terminology. Axioms and schemes of the theory of sets.
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16. Set theory [2003]
 Jech, Thomas J.
 The 3rd millennium ed., rev. and expanded.  Berlin ; New York : Springer, c2003.
 Description
 Book — xiii, 769 p. ; 24 cm.
 Summary

 I. Basic Set Theory. Axioms of Set Theory. Ordinal Numbers. Cardinal Numbers. Real Numbers. The Axiom of Choice and Cardinal Arithmetic. The Axiom of Regularity. Filters, Ultrafilters and Boolean Algebras. Stationary Sets. Combinatorial Set Theory. Measurable Cardinals. Borel and Analytic Sets. Models of Set Theory. II. Advanced Set Theory. Constructible Sets. Forcing. Applications of Forcing. Iterated Forcing and Martin's Axiom. Large Cardinals. Large Cardinals and L. Iterated Ultrapowers and LAUU. Very Large Cardinals. Large Cardinals and Forcing. Saturated Ideals. The Nonstationary Ideal. The Singular Cardinal Problem. Descriptive Set Theory. The Real Line. III. Selected Topics. Combinatorial Principles in L. More Applications of Forcing. More Combinatorial Set Theory. Complete Boolean Algebras. Proper Forcing. More Descriptive Set Theory. Determinacy. Supercompact Cardinals and the Real Line. Inner Models for Large Cadinals. Forcing and Large Cardinals. Martin's Maximum. More on Stationary Sets. Bibliography. Notation. Index. Name Index.
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Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA248 .J42 2003  CHECKEDOUT 
17. Set theory [electronic resource] [2003]
 Jech, Thomas J.
 The 3rd millennium ed., rev. and expanded.  Berlin ; New York : Springer, c2003.
 Description
 Book — xiii, 769 p.
18. Sets for Mathematics [electronic resource]. [2003]
 Cambridge : Cambridge University Press, 2003.
 Description
 Book — 1 online resource (276 p.) : digital, PDF file(s).
 Summary

 Foreword
 1. Abstract sets and mappings
 2. Sums, monomorphisms and parts
 3. Finite inverse limits
 4. Colimits, epimorphisms and the axiom of choice
 5. Mapping sets and exponentials
 6. Summary of the axioms and an example of variable sets
 7. Consequences and uses of exponentials
 8. More on power sets
 9. Introduction to variable sets
 10. Models of additional variation
 Appendices
 Bibliography.
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19. Basic set theory [2002]
 Osnovy teorii mnozhestv. English
 Shen, A. (Alexander), 1958
 Providence, R.I. : American Mathematical Society, c2002.
 Description
 Book — viii, 116 p. : ill. ; 22 cm.
 Summary

 Sets and their cardinalities Ordered sets Bibliography Glossary Index.
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SAL3 (offcampus storage)
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QA248 .V4613 2002  Available 
20. Teoría de conjuntos [2002]
 Tiñena Salvañà, Francesc, author.
 [Barcelona] : UOC, la universidad virtual, [2002]
 Description
 Book — 1 online resource (43 pages).
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