Reflections on the foundations of mathematics : univalent foundations, set theory and general thoughts /: univalent foundations, set theory and general thoughts. ([2019])

• Record Type: Book
• Further Information: Note: Stefania Centrone, Deborah Kant, Deniz Sarikaya, editors.
• Editors: Centrone, Stefania; Kant, Deborah; Sarikaya, Deniz
• Contents: Intro; Introduction; The Topic; Historical Background; Current Foundations; Set Theory; Homotopy Type Theory/Univalent Foundations; The Contributions; Part I: Current Challenges for the Set-Theoretic Foundations; Part II: What are Homotopy Type Theory and the Univalent Foundations?; Part III: Comparing Set theory, Category Theory, and Type Theory; Part IV: Philosophical Thoughts on the Foundations of Mathematics; Part V: Foundations in Mathematical Practice; The Editors; Literature; Contents; Part I Current Challenges for the Set-Theoretic Foundations; 1 Interview With a Set Theorist Introduction1.1 Introduction; 1.2 Methodological Background; 1.2.1 How to Describe and Analyse Set-Theoretic Practice?; 1.2.2 Why Describe and Analyse Set-Theoretic Practice?; 1.3 Preliminary Facts; 1.4 Some Important Forcing Results; 1.4.1 Cohen's Introduction of Forcing; 1.4.2 Important Forcing Results; 1.4.2.1 Easton Forcing; 1.4.2.2 Suslin's Hypothesis, Iterated Forcing and Martin's Axiom; 1.4.2.3 Laver Forcing; 1.4.2.4 Proper Forcing and Proper Forcing Axiom; 1.5 Philosophical Thoughts in Set Theory; 1.6 Set-Theoretic Intuition About Independence; 1.7 Conclusion; References; References 2 How to Choose New Axioms for Set Theory?2.1 Introduction; 2.2 Ordinary Mathematics; 2.3 Intrinsic Motivations; 2.4 Extrinsic Motivations; 2.5 The Axiom of Constructibility; 2.6 Large Cardinals Axioms; 2.7 Measurable Cardinals and Elementary Embeddings; 2.8 Determinacy Hypotheses; 2.9 Ultimate L and Forcing Axioms; 2.10 Conclusion; References; 3 Maddy On The Multiverse; 3.1 The Problem; 3.2 Multiverse Conceptions; 3.2.1 Naive Multiversism; 3.2.2 Instrumental Multiversism; 3.2.3 Ontological Multiversism; 3.3 Maddy's Assessment of the Multiverse; 3.4 Addressing the Problems
• Publisher Details: Cham : Springer Nature
• Publication Date: 2019
• Copyright Date: 2019
• Extent: 1 online resource (510 pages)
• Subjects: 511.3/22; Set theory; Logic, Symbolic and mathematical; Electronic books; Electronic books
• Languages: English
• ISBNs: 3030156559; 9783030156558
• Related ISBNs: 9783030156541
• Notes: Note: References to Reply to Ternullo on the Multiverse4 Proving Theorems from Reflection; 4.1 Introduction; 4.2 The Task to Hand; 4.2.1 The Baire and Perfect Subset Properties; 4.2.2 Uniformisation; 4.2.3 The Banach-Tarski Property; 4.3 Difficulties; 4.4 Resolution and Reflection; 4.4.1 Resolution; 4.4.2 Reflection; 4.4.2.1 Global Reflection Principle: GRP; 4.5 Discussion; References; Part II What Are Homotopy Type Theory and the Univalent Foundations?; 5 Naïve Type Theory; 5.1 Introduction; 5.2 Type Theory vs Set Theory; 5.3 Non-dependent Types; 5.3.1 Universes; 5.3.2 Functions; Note: Includes bibliographical references.; Note: Description based on online resource; title from digital title page (viewed on November 21, 2019).
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