Finitely Supported Mathematics An Introduction
In this book the authors present an alternative set theory dealing with a more relaxed notion of infiniteness, called finitely supported mathematics (FSM). It has strong connections to the Fraenkel-Mostowski (FM) permutative model of Zermelo-Fraenkel (ZF)
- PDF / 1,770,321 Bytes
- 188 Pages / 453.543 x 683.15 pts Page_size
- 55 Downloads / 214 Views
nitely Supported Mathematics An Introduction
Finitely Supported Mathematics
Andrei Alexandru Gabriel Ciobanu •
Finitely Supported Mathematics An Introduction
123
Gabriel Ciobanu Institute of Computer Science Romanian Academy Iaşi, Romania
Andrei Alexandru Institute of Computer Science Romanian Academy Iași, Romania
ISBN 978-3-319-42281-7 DOI 10.1007/978-3-319-42282-4
ISBN 978-3-319-42282-4
(eBook)
Library of Congress Control Number: 2016946318 © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
Contents
1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Approaches Related to the Fraenkel-Mostowski Framework . . . . . . . 1.3 Finitely Supported Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 1 5 7 9
2
Fraenkel-Mostowski Set Theory: A Framework for Finitely Supported Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Axiom of Choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Permutative Renaming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Sets with Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Constructions of Sets with Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Powersets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Cartesian Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Data Loading...
