Article View: fj.sci.math
Article #14247Re: foundation axiom (Re: two "simple" questions)
From: Yoshinori TANABE
Date: Fri, 12 Mar 1993 08:34
Date: Fri, 12 Mar 1993 08:34
58 lines
3425 bytes
3425 bytes
$@EDJU!wIY;NDL@n:j(J$@9)>l(J $@$G$9!%(J
>>Message-ID: <SHIMURA.93Mar10214412@octopus.cst.nihon-u.ac.jp> $@$N5-;v$G(J,
>>$@;VB<(J( shimura@cst.nihon-u.ac.jp )$@$5$s(J:
$@;VB<(J> $@$3$3$G$$$&(J $@%0%i%U(J (G,R) $@$,(J extensional $@$G$"$k$H$O!"<!$N$3(J
$@;VB<(J> $@$H(J$@$@$H;W$$$^$9!#(J
$@;VB<(J> a,b in G $@$N(J R $@$K$+$s$9$k(J $@?d0\E*JDJq$r$=$l$>$l(Jcl(a), cl(b)
$@;VB<(J> $@$H$7$?$H$-!"(J R $@$N(J cl(a), cl(b) $@$X$N@)8B$,(J"$@%0%i%U$H$7$F(J"$@F17?(J
$@;VB<(J> $@$J$i$P!"(Ja=b $@$G$"$k!#(J
($@N,(J)
$@;VB<(J> $@IaDL(J extensional $@$H(J$@$$$&$H$-$O!"(J{x : xRa}={x : xRb} $@$J$i$P(J
$@;VB<(J> a=b $@$r;X$9$H;W$&$N$G!"$3$N2r<a$N2<$G$O<B?t$N=89g$O(J
$@;VB<(J> extensional $@$@$1$l$I$b!"%0%i%U$H$7$F$O$=$&$G$O$J$$$H$$$&$3(J
$@;VB<(J> $@$H$G$7$g$&!#(J
$@$J$k$[$I$J$k$[$I!%(J
$@$H8@$C$H$$$F$J$s$G$9$,!$MQ8l$N3NG'$r$5$;$F2<$5$$!%(J
(1) cl(a)$@$H$$$&$N$O(J
x_0 = {a}
x_(n+1) = {b \in G | bRy $@$J$k(J y \in x_n $@$,$"$k(J}
$@$HCV$$$?;~$N(J \bigcup{x_n | n $@$O<+A3?t(J} $@$N$3$H$G$9$M!%(J
(2) (G_1,R_1)$@$H(J(G_2,R_2)$@$,%0%i%U$H$7$FF17?$G$"$k$H8@$&$N$O!$(J
f:G_1->G_2 $@$J$kA4C1<M$,B8:_$7$F(J
<g,h> \in R_1 iff <f(g),f(h)> \in R_2
$@$H$$$&$3$H$G$h$$$G$9$+!)(J
$@;d$,5?Ld$K;W$C$F$$$k$N$O!$>e$NDj5A$G$$$/$H(J
(G,R) = ({0,1},{<0,0>,<0,1>,<1,1>})
$@$_$?$$$J%0%i%U$O(J extensional $@$K$J$C$F$7$^$&$1$I!$$=$l$G$bNI(J
$@$$$N$+$J!)$H(J$@$+!$(J
>>Message-ID: <SATOSHI.93Mar9193044@whale.math.ryukoku.ac.jp> $@$N5-;v$G(J,
>>$@>.NS(J( satoshi@whale.math.ryukoku.ac.jp )$@$5$s(J:
$@>.NS(J> $@$K$7$F$*$$$F$+$i$d$l$P$$$$$o$1$G$9!#$3$3$G!"E,Ev$H$$$C$?$N$O!"@53N$K(J$@$O!"(J
$@>.NS(J> $@F1CM4X78$G3d$C$?;~$K(J extensional $@$K$J$k$h$&$J:G>.$NF1CM4X78$G3d$k$o$1(J
$@>.NS(J> $@$G$9!#(J
$@!V:G>.(J$@$NF1CM4X78!W$,B8:_$9$k$H$O8B$i$J$$$h$&$K;W$o$l$k$H$+$G(J
$@$9!%(J
$@;VB<(J> extensional $@$J%0%i%U$@$1$r9M$($l$P(J$@NI$$$H$$$&$N$O!"(JAFA $@$K$*(J
$@;VB<(J> $@$1$k<LA|(J d $@$N0l0U@-$H!"301d@-8xM}(J (axiom of extensionality)
$@;VB<(J> $@$+$i(J$@$N5"7k$@$H;W$$$^$9!#(J
$@!V(Jextensional$@$J%0%i%U$@$1$r9M$($l$PNI$$!W$H$$$&$N$O!$!V(JAFA$@$N(J
$@%9%F!<%H%a%s%H$K$*(J$@$$$F!$(J``$@$9$Y$F$N%0%i%U(J''$@$r(J``$@$9$Y$F$N(J
extensional$@$J%0%i%U(J''$@$KCV$-49$($F$bL?Bj$N6/$5$OJQ$o$i$J$$!W(J
$@$H$$(J$@$&0UL#$G$7$g$&$+!)(J
--
| $@EDJU(J $@NIB'(J $@!w(J $@IY;NDL(J $@@n:j9)>l(J
| E-mail: tanabe@ai.cs.fujitsu.co.jp
Technical Details
Message-ID:
<TANABE.93Mar12173435@Polaris.ai.cs.Fujitsu.Co.JP>Path:
arc1-ca.pugleaf.net!sparky!uunet!spool.mu.edu!sdd.hp.com!sgiblab!nec-gw!nec-tyo!wnoc-tyo-news!sh.wide!fgw!fdm!csnews!virgo!tanabeReferences:
<SATOSHI.93Mar9193044@whale.math.ryukoku.ac.jp> <SHIMURA.93Mar10214412@octopus.cst.nihon-u.ac.jp>Show Full Headers
Complete Article Headers
X-Google-Language: Japanese,JIS X-Google-Thread: f4956,38f3806df9a3b430 X-Google-Attributes: gidf4956,public X-Google-ArrivalTime: 1993-03-12 01:10:20 PST Path: arc1-ca.pugleaf.net!sparky!uunet!spool.mu.edu!sdd.hp.com!sgiblab!nec-gw!nec-tyo!wnoc-tyo-news!sh.wide!fgw!fdm!csnews!virgo!tanabe From: tanabe@ai.cs.Fujitsu.Co.JP (Yoshinori TANABE) Newsgroups: fj.sci.math Subject: Re: foundation axiom (Re: two "simple" questions) Message-ID: <TANABE.93Mar12173435@Polaris.ai.cs.Fujitsu.Co.JP> Date: 12 Mar 93 08:34:35 GMT References: <SATOSHI.93Mar9193044@whale.math.ryukoku.ac.jp> <SHIMURA.93Mar10214412@octopus.cst.nihon-u.ac.jp> Sender: news@ai.cs.fujitsu.co.jp Distribution: fj Organization: Fujitsu Ltd., Kawasaki Japan Lines: 58 In-reply-to: shimura@cst.nihon-u.ac.jp's message of 10 Mar 93 21:44:12 JST