//img.uscri.be/pth/9649f4ba12edfb9004cfd8222559580be39f5890
Cette publication ne fait pas partie de la bibliothèque YouScribe
Elle est disponible uniquement à l'achat (la librairie de YouScribe)
Achetez pour : 18,00 € Lire un extrait

Lecture en ligne (cet ouvrage ne se télécharge pas)

PROCEEDINGS OF THE 70TH ANNIVERSARY NF MEETING IN CAMBRIDGE

173 pages

This cahier contains almost all the contributions to the two day meeting, commemorating the 70th year of the publication of Quine's seminal paper “New Foundations for Mathematical Logic”, in which he describes for the first time the remarkable set theory

Publié par :
Ajouté le : 01 juin 2012
Lecture(s) : 0
EAN13 : 9782296492356
Signaler un abus
NF
PROCEEDINGS
70
TH
OF
THE
ANNIVERSARY
MEETING
IN
CAMBRIDGE
e´puise´ ´epuis´e ´epuis´e ´puie´ e s e´puise´ epuise´ ´ ´i´e epu s
D´j` parus e a Cahier 1 Intuitionnismeetth´eoriedelade´monstration. Cahier 2 Textes de Jean Pieters. Cahier 3 J.-L. Moens, Forcingets´emantiquedeKripkeJoyal. Cahier 4 Lath´eoriedesensemblesdeQuine. Cahier 5 T. E. Forster, Quine’s New Foundations. Cahier 6 Logique et informatique. Cahier 7 Lantifondationenlogiqueetenth´eoriedesensembles. Cahier 8 Ph. de Groote (ed.), The Curry–Howard Isomorphism. Cahier 9 A.P´etry(´ed.), Me´thodesetanalysenonstandard. Cahier 10 ´epuis´e M. R. Holmes, Elementary Set Theory with a Universal Set. Cahier 11 Chr. Michaux (ed.), Definability in Arithmetics and Computability. Cahier 12 P. Van Praag, Aspectsdeladualite´enmathe´matique. Cahier 13 O. Esser, Uneth´eoriepositivedesensembles. Cahier 14 K. De Clercq, Logica in communicatie. Cahier 15 S. Richard, Laconceptions´emantiquedelav´erite´ Uneversione´lectroniquedesvolumese´puis´esseraprochainement disponible sur http://www.logic-center.be/cahiers .
Log16FT
CAHIERS DU CENTRE DE LOGIQUE 16
PROCEEDINGS OF THE 70 TH ANNIVERSARY NF MEETING IN CAMBRIDGE
Marcel CRABBÉ and Thomas FORSTER (eds)
Centre National de Recherches de Logique Nationaal Centrum voor Navorsingen in de Logica
 
1
L O U VA I N - L A - N E U V E
10/14/09, 6:30 PM
2 0 0 9
CAHIERS DU CENTRE DE LOGIQUE
Directeur de la collection : ´ M. Crabbe Comit´ed´daction: e re D. Batens , M.Crabb´e,J.DeGreef,Ph.deGroote (Nancy), D. Dzierzgowski, T. E. Forster (Cambridge), R. Hinnion, M. R. Holmes (Boise), Th. Lucas, J. Meheus, Chr.MichA.P´etry. aux,
Cahier16e´dit´epar: MarcelCrabbe´etThomasForster, Universit´ecatholiquedeLouvain,UniversityofCambridge.
Secre´tariat: D. Servais
Composition : D. Dzierzgowski
Centre national de recherches de logique http://www.logic-center.be/cahiers
D/2009/4910/44 ISBN 978–2–87209–937–5
c BRUYLANT-ACADEMIA s.a. Grand-Place 29 B–1348 Louvain-la-Neuve
Tousdroitsdereproduction,dadaptationoudetraduction,parquelqueproc´ede´que cesoit,re´serve´spourtouspayssanslautorisationdele´diteur. Imprim´eenBelgique.
Foreword
This cahier contains almost all the contributions to the two day meeting, commemorating the 70th year of the publication of Quine’s seminal paper “New Foundations for Mathematical Logic”, in which he describes for the first time the remarkable set theory NF. It contains also some other contributions which were prompted by this meeting. This meeting follows the 50th meeting held in Oberwolfach in 1987, orga-nized by M. Boffa and E. Specker in the presence of Quine, and the 60th anniversary meeting in Cambridge in 1997. The two first papers : “A permutation method yielding models of the stratified axioms of Zermelo Fraenkel set theory”, and “Permutation me-thods in NF and NFU”, are concerned with permutation techniques and unstratified formulæ. In “There is a Forster term model of simple type theory”, M. R. Holmes shows a model of type theory wherein all elements are the denotations of closed terms. InAmbiguousCardinalsandNFandindiscerniblesinZF,M.Crabb´e and S. Tupailo, show how to export results arising in NF to standard set theory. The paper “Combinatorics related to NF consistency”, by A. Tzouvaras, explores different combinatorial techniques in order to reduce the consis-tency problem of NF. The cahier ends with T. E. Forster’s tutorial on Constructive NF.
The Editors
Contents
V. H. Dang and Z. McKenzie A permutation method yielding models of the stratified axioms of Zermelo Fraenkel set theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
T. E. Forster and M. R. Holmes Permutation methods in NF and NFU . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
M. R. Holmes There is a Forster term model of Simple Type Theory . . . . . . . . . . . . . 77
M. C ´ rabbe Ambiguous cardinals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
S. Tupailo NF and indiscernibles in ZF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
A. Tzouvaras Combinatorics related to NF consistency . . . . . . . . . . . . . . . . . . . . . . . . . 109
T. E. Forster A tutorial on Constructive NF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Cahiers du Centre de logique Volume 16
A permutation method yielding models of the stratified axioms of Zermelo Fraenkel set theory
by
V. H. Dang and Z. McKenzie University of Cambridge
1. Introduction This paper endeavours to survey some of the recent work investigating models of the stratified axioms of Zermelo-Fraenkel Set Theory (ZF). Specifically we will focus on a hybridisation of the Fraenkel-Mostowski-Specker and Rieger-Bernays permutation techniques developed by Thomas Forster to produce models of the stratified fragment of ZF refuting certain unstratified axioms. The major motivation is the hope that models of frag-ments of stratified comprehension will shed some light on the consistency strength of Quine’s “New Foundations” (NF). The job of completely under-standing and exploring generalisations of Forster’s technique is nowhere near completion, by any stretch of the imagination. We will paint the partial picture representing our present understanding as an overture to discussing some of the important and interesting open problems in this research. Any results discussed in the paper that are attributed to an individual, but not referenced to a published text, have emerged in dis-cussions on this subject held at Cambridge University.