Positive Topology

A New Practice in Constructive Mathematics

Inbunden, Engelska, 2025

2 049 kr

Beställningsvara. Skickas inom 5-8 vardagar. Fri frakt för medlemmar vid köp för minst 249 kr.

Aimed at researchers in mathematics, philosophy and logic, this book provides the first organic exposition of dynamic constructivism and the mathematics ensuing in practice, including discussion of the technical development of the field and outlining the philosophical and methodological motivations underlying the evolution of the discipline.In dynamic constructivism, mathematics is seen as the result of a dynamic process of interaction between the construction of mathematical entities, by abstraction and by idealization, and their selection according to their efficiency in applications to reality and in the organisation of mathematics itself.The crucial benefit of this vision is its independence from dogmas and external authorities. A practical consequence is full respect for the diverse areas of mathematics - mainly computation, spatial intuition, deduction, and abstract axiomatic method - without reducing one to another. As a second consequence, a dynamic interaction between different 'epistemological levels' is always active and present, in the development of mathematics in practice, the study of its foundations and its formalisation in a computer language.

Produktinformation

Utgivningsdatum2025-10-30
Mått160 x 240 x 36 mm
Vikt1 199 g
FormatInbunden
SpråkEngelska
SerieOxford Logic Guides
Antal sidor656
FörlagOUP OXFORD
ISBN9780199232888

Tillhör följande kategorier

Giovanni Sambin has been doing research in logic and the foundations of mathematics since the 1970s. He is among the founders of provability logic and has been developing the field of topology since the 1990s, adopting a dynamic view in mathematical practice, leading to positive topology, a new, richer approach to constructive topology based on a dynamic vision of the nature of mathematics. He was the first president of the Italian Association of Logic and its Applications (AILA).

PrefaceAbout This Book1: Dynamic Constructivism: A New Conception of Mathematics2: The Minimalist Foundation: Basic Notions and Tools3: Basic Pairs: Symmetry and Duality in Topology4: Relation-Pairs: Continuity is a Commutative Square5: Concrete Spaces: Benefits of Keeping a Base6: Convergent Relation-Pairs: Towards Topology With Points7: Basic Topologies: Pointfree Topology Without Convergence8: Continuous Relations: Respecting Covers and Positivities9: Positive Topologies and Formal Maps: Pointfree Topology10: Ideal Spaces and Maps: Ideal Aspects Over Real Topology11: Topological Systems: a Place for all Topological Notions12: Overlap Algebras: the Power of a Set as an Algebra13: Overlap Topologies: Putting Topology in Algebraic TermsAppendix A: Generating Positivity By Co-inductionReferencesIndex

Mer från samma författare

Del 36

Twenty Five Years of Constructive Type Theory

Giovanni Sambin, Jan M. Smith, Italy) Sambin, Giovanni (Professor of Mathematical Logic, Professor of Mathematical Logic, University of Padua, Sweden) Smith, Jan M. (Professor, Department of Computing Science, Professor, Department of Computing Science, Chalmers University of Technology, Jan Smith

Inbunden

1 589 kr

Mer från samma serie

Consequence Relations

Alex Citkin, Alexei Muravitsky, New York) Citkin, Alex (CIO, CIO, Metropolitan Telecommunications, Louisiana Scholars' College at Northwestern State University of Louisiana) Muravitsky, Alexei (Professor of Mathematics, Professor of Mathematics

Inbunden

1 609 kr

Fragments of First-Order Logic

Ian Pratt-Hartmann, University of Opole) Pratt-Hartmann, Ian (Senior Lecturer, University of Manchester Professor of Mathematical Sciences, University of Opole, Senior Lecturer, University of Manchester Professor of Mathematical Sciences

Inbunden

2 309 kr

Del 24

Introduction to Logic and to the Methodology of Deductive Sciences

Alfred Tarski, The late Alfred Tarski, Jan Tarski

Inbunden

2 159 kr

Del 19

Gödel's Incompleteness Theorems

Raymond M. Smullyan, USA) Smullyan, Raymond M. (Professor, City College, Professor, City College, City University of New York

Inbunden

4 289 kr

Del 22

Recursion Theory for Metamathematics

Raymond M. Smullyan, Indiana University) Smullyan, Raymond M. (Professor of Philosophy, Professor of Philosophy

Inbunden

2 859 kr

Del 36

Twenty Five Years of Constructive Type Theory

Inbunden

1 589 kr

Del 42

Change, Choice and Inference

Hans Rott, Germany) Rott, Hans (, Professor of Philosophy, University of Regensburg

Inbunden

3 139 kr

Del 38

Fibring Logics

Dov M. Gabbay, London) Gabbay, Dov M. (Professor of Computer Science, Professor of Computer Science, King's College

Inbunden

1 979 kr

Del 39

Elements of Intuitionism

Michael Dummett, University of Oxford) Dummett, Michael (Emeritus Professor of Philosophy, Emeritus Professor of Philosophy

Inbunden

4 669 kr

Del 46

Interpolation and Definability

Dov M. Gabbay, Larisa Maksimova, King's College London) Gabbay, Dov M. (, Department of Computer Science, Russia) Maksimova, Larisa (, Institute of Mathematics, Siberian Branch of Russian Academy of Science, Novosibirsk

Inbunden

3 619 kr

Du kanske också är intresserad av

Del 36

Twenty Five Years of Constructive Type Theory

Inbunden

1 589 kr

Del 21

Elementary Categories, Elementary Toposes

McLarty, Colin McLarty

Häftad

2 119 kr

Del 30

Features and Fluents

Erik Sandewall, Sweden) Sandewall, Erik (Professor, Department of Computer and Information Science, Professor, Department of Computer and Information Science, Linkoping University

Inbunden

1 909 kr