Algebraic Set Theory

Andri Joyal, Ieke Moerdijk (Autoren)

Buch | Softcover

132 Seiten

1995
Cambridge University Press (Verlag)
978-0-521-55830-3 (ISBN)

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Offers a new, algebraic, approach to set theory. The authors introduce a particular kind of algebra, the Zermelo-Fraenkel algebras, which arise from the familiar axioms of Zermelo-Fraenkel set theory. Furthermore the authors explicitly construct such algebras using the theory of bisimulations. Their approach is completely constructive, and contains both intuitionistic set theory and topos theory.

This book offers a new, algebraic, approach to set theory. The authors introduce a particular kind of algebra, the Zermelo-Fraenkel algebras, which arise from the familiar axioms of Zermelo-Fraenkel set theory. Furthermore the authors explicitly construct such algebras using the theory of bisimulations. Their approach is completely constructive, and contains both intuitionistic set theory and topos theory. In particular it provides a uniform description of various constructions of the cumulative hierarchy of sets in forcing models, sheaf models and realisability models. Graduate students and researchers in mathematical logic, category theory and computer science should find this book of great interest, and it should be accessible to anyone with some background in categorical logic.

1. Axiomatic theory of small maps; 2. Zermelo-Fraenkel algebras; 3. Existence theorems; 4. Examples.

Erscheint lt. Verlag	14.9.1995
Reihe/Serie	London Mathematical Society Lecture Note Series
Zusatzinfo	Worked examples or Exercises
Verlagsort	Cambridge
Sprache	englisch
Maße	154 x 229 mm
Gewicht	210 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
ISBN-10	0-521-55830-1 / 0521558301
ISBN-13	978-0-521-55830-3 / 9780521558303
Zustand	Neuware