The Hyperuniverse Project and Maximality [electronic resource] /
Antos, Carolin.editor.
Friedman, Sy-David.editor.
Honzik, Radek.editor.
Ternullo, Claudio.editor.
This collection documents the work of the Hyperuniverse Project which is a new approach to set-theoretic truth based on justifiable principles and which leads to the resolution of many questions independent from ZFC. The contributions give an overview of the program, illustrate its mathematical content and implications, and also discuss its philosophical assumptions. It will thus be of wide appeal among mathematicians and philosophers with an interest in the foundations of set theory. The Hyperuniverse Project was supported by the John Templeton Foundation from January 2013 until September 2015.
Includes bibliographical references at the end of each chapters.
Class forcing in Class Theory -- Hyperclass Forcing in Morse-Kelley Class Theory -- Multiverse conceptions in set theory -- Evidence for set-theoretic truth and the Hyperuniverse Programme -- On the set-generic multiverse -- Mathematical Logic Quarterly -- Definability of satisfaction in outer models -- The search for new axioms in the Hyperuniverse Programme, in Philosophy of Mathematics: objectivity, cognition and proof -- Explaining maximality through the Hyperuniverse Programme.
This collection documents the work of the Hyperuniverse Project which is a new approach to set-theoretic truth based on justifiable principles and which leads to the resolution of many questions independent from ZFC. The contributions give an overview of the program, illustrate its mathematical content and implications, and also discuss its philosophical assumptions. It will thus be of wide appeal among mathematicians and philosophers with an interest in the foundations of set theory. The Hyperuniverse Project was supported by the John Templeton Foundation from January 2013 until September 2015.
Mathematical logic.
Mathematics-Philosophy.
Mathematical Logic and Foundations.
Philosophy of Mathematics.