Article View: fj.sci.math
Article #14267Re: two "simple" questions
From: Satoshi Kobayashi
Date: Sat, 20 Mar 1993 02:57
Date: Sat, 20 Mar 1993 02:57
67 lines
4205 bytes
4205 bytes
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In article <1993Mar18.104242.3055@etl.go.jp> yoshiki@etl.go.jp
(KINOSHITA Yoshiki) writes:
|$@!V=89gO@$r!J=89gO@0J30$N!K?t3X$N4pAC$H$9$k$3$H$K5?Ld(J$@$,$"$k!W$H$$$&4QE@(J
|$@$+$i!"(Jnon-well-founded set $@$X$N(J objection $@$H$7$F<!$NO@J8$,LLGr$+$C$?$N(J
|$@$G>R2p$7(J$@$^$9!#(J
|
| Michael Barr: Functional set theory
|
| FTP-able from `triples.math.mcgill.ca' (132.206.150.30),
| directory `Barr', file `math_intelligencer.ps'
|
|Mathematical intelligencer $@$H(J$@$$$&;(;o$K=P$?5-;v$N$h$&$G$9!#(J
$@$3$l$OLLGr$=$&$G$9$M!#9qFb$N$I$3$+$+$i(J FTP $@$G$-$J$$$N$G$7$g$&$+!#:#(J
archie $@$7$F$_$?=j$G$O$=$l$i$7$$$N$O$J$$$h$&$G$9$,!#(J
|Barwise & Moss $@$K$h$k!V(JA$@!_(JX$@!a(JX $@$N$h$&$JNN0hJ}Dx(J$@<0$r(J non-well-founded
|set $@$G2r$1$k$h!W$H$$$&O@J8$rFI$s$G!"(J
|
| The purpose of this note is to suggest that the whole
| enterprise is wrong-headed
|
|$@$H$$$&$3$H$@$=$&$G$9!#6/Nu$d$J$"!#(JNon-well-founded sets $@$G$NK\Ev$NLdBj(J
$@3N$+$K$:$$$V$s6/Nu$J=q$-J}$G$9$M!#(J
|$@E@$O!"(J
|
| the irrelevance of actual elements in mathematics
|
|$@$@!"$H$$$&$N$,O@E@$G!"$3$NO@J8$G$O!"=89g$N$D$/$k7w$N8xM}$rM?$($F(J$@!J%H%](J
|$@%9!\&A!K!"$=$N8xM}$N$b$H$GNN0hJ}Dx<0$r2r$$$F$_$;$F$$$^$9!#$3$l<+BN$O0l(J
|$@Dj$N>r7o$rK~$?$97w$G(J$@NN0hJ}Dx<0$r2r$/$H$$$&$3$H$G!"FC$KL\?7$7$/$O$"$j$^(J
|$@$;$s$,!"$H$K$+$/(J non-well-founded set $@$K$h$k0J30(J$@$N2r$K$J$C$F$$$^$9!#!_(J
|$@!\"*$/$i$$$+$i$J$kNN0hJ}Dx<0$J$i(J Scott $@M}O@$G$b2r$1$^$9$,!#(J
$@:#;W$C$?$N$G$9$1(J$@$I!"(JX = N + (X -> X) $@$_$?$$$J$N$O!"(Jnon-well-founded
sets $@$G2r$1$^$7$?$C$1(J? $@$?$@$7!"(JN $@$O<+A3?t$N=89g$N(J$@$D$b$j$G$9!#;d$O(J
Aczel $@$NK\$b<B$O$=$l$[$I$A$c$s$HFI$s$G$J$$$7!":#<j85$K$b$J$$(J($@A0$K?^=q(J
$@4[$+$i<Z$j$F$$(J$@$?$1$l$IJV$7$F$7$^$$$^$7$?(J)$@$N$G!"$h$/$o$+$j$^$;$s$1$I!D!#(J
classical logic $@$G9M$($F$$$k$+$iG;EY$r9M$($k(J$@$H$@$a$J$h$&$J!D!#(JScott $@M}(J
$@O@$@$H4X?t6u4V$N0UL#$rO"B3$J4X?t$N6u4V$K@)8B$9$k$+$i(J OK $@$@$1$l$I$b!#(J
non-well-founded sets $@$O%i%`%@7W;;$N2r<a$K$&$^$/MxMQ$G$-$k!"$H$$$&OC$O(J
$@A0$+$i$"$k$h$&$G$9$,!">e$N$h$&$JJ}(J$@Dx<0$r(J($@$-$C$A$jN>JU$,Ey$7$/$J$k$h$&$K(J)
$@2r$1$k!"$H$$$&OC$K$O$J$C$F$J$+$C$?$h$&$J!#(J
$@0lJ}!"D>4Q<g5AO@M}(J$@$K$7$F$7$^$&$H!"G;EY$NLdBj$K0z$C$+$+$i$:!"<B:]!">e$N(J
$@$h$&$JJ}Dx<0$K2r$,$"$k$h$&$J=89gO@$N%b%G%k$,$"$k(J$@!"$H$$$&$N$O$@$s$V$sA0(J
$@$+$iCN$i$l$F$$$k;v$@$H;W$$$^$9!#;d$,6=L#$,$"$k$N$O!">e$N(J Barr $@$5$s$N$d(J
$@$jJ}$@$H(J$@$A$c$s$H2r$1$k$N$+!"2r$1$k$H$7$?$i!"$=$N$?$a$KLrN)$C$F$$$k;E3](J
$@$1$O2?$+!"$H$$$&$3$H$G$9!#%H%]%9(J + \alpha $@$H$$$&$3$H$@$+$i!"D>4Q<g5AO@(J
$@M}$,%Y!<%9$J$N$+$b!D!#(J
|$@=89g$G$d$k$H!"6qBNE*$9$.$k!"(Jsets have too much structure $@$H$$$&$N$,H`(J
|$@$N7kO@$G$9!#(J
$@$(!<!"$3$NItJ,$K$b%3%a%s%H$7$?$$$N$G$9$,!":#$A$g$C$H;~4V$,(J$@$J$/$J$C$F$-(J
$@$?$N$G!":#EY$b$7;~4V$,$"$C$?$i2?$+=q$-$^$9!#$G$O!#(J
--
$@N6C+Bg3XM}9)3XIt?tM}>pJs3X2J(J $@>.NS(J $@Ao(J |
satoshi@rins.ryukoku.ac.jp | <- $@%"%I%l%9$rJQ$($^$7$?$,!"EvJ,$O(J
0775-43-7523($@3X2J;vL3(J$@<<(J) 7528($@8&5f<<(J) | $@A0$N(J satoshi@whale.ryukoku.ac.jp
7524(FAX) | $@$G$b(J$@FO$-$^$9!#(J
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<SATOSHI.93Mar20115742@whale.math.ryukoku.ac.jp>Path:
arc1-ca.pugleaf.net!sparky!uunet!stanford.edu!sun-barr!sh.wide!wnoc-kyo!rinsgw!rins!satoshiReferences:
<1993Feb20.053151.28144@kudpc.kyoto-u.ac.jp> <SATOSHI.93Feb25185120@whale.math.ryukoku.ac.jp> <1993Mar16.025147.27136@kudpc.kyoto-u.ac.jp> <1993Mar18.104242.3055@etl.go.jp>Show Full Headers
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X-Google-Language: Japanese,JIS X-Google-Thread: f4956,38f3806df9a3b430 X-Google-Attributes: gidf4956,public X-Google-ArrivalTime: 1993-03-19 19:29:02 PST Path: arc1-ca.pugleaf.net!sparky!uunet!stanford.edu!sun-barr!sh.wide!wnoc-kyo!rinsgw!rins!satoshi From: satoshi@whale.math.ryukoku.ac.jp (Satoshi Kobayashi) Newsgroups: fj.sci.math Subject: Re: two "simple" questions Message-ID: <SATOSHI.93Mar20115742@whale.math.ryukoku.ac.jp> Date: 20 Mar 93 02:57:42 GMT References: <1993Feb20.053151.28144@kudpc.kyoto-u.ac.jp> <SATOSHI.93Feb25185120@whale.math.ryukoku.ac.jp> <1993Mar16.025147.27136@kudpc.kyoto-u.ac.jp> <1993Mar18.104242.3055@etl.go.jp> Sender: news@rins.ryukoku.ac.jp Distribution: fj Organization: Ryukoku Univ., Seta, Otsu, Japan Lines: 67 In-reply-to: yoshiki@etl.go.jp's message of 18 Mar 93 10:42:42 GMT