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Article View: fj.sci.math
Article #14316

Re: Q in intuitionistic math.

#14316
From: Satoshi Kobayashi
Date: Mon, 30 Nov 1992 10:22
59 lines
3581 bytes
$@>.NS(J@$@N6C+Bg3X$G$9!#(J

In article <RYU.92Nov28090325@sysipk.sys.titech.ac.jp> ryu@sys.titech.ac.jp (ryu) writes:

 | |b$@$,(Ja$@$NItJ,%/%i%9$H$7$F(J
 | |$@$"$k(Jf:A->Bool$@$r$H$C$F(J
 | |f_inverse({true})$@$H(Jb$@$,F1$8301d$r$b$D$H(J$@$O$+$.$i$J$$(J
 | |$@$H$$$&$3$H$G!"$?$H$($P!"8EE5=89gO@$G$O(J
 | |f(x)= true (x in b)
 | |    = false (Not(x in b))
 | |$@$G>l9gJ,$1$9$k$3$H$G!"(Jb$@$KBP1~$9$k(Jf$@$,$D$/$l$^$9$,(J
 | |$@D>4Q<g5A$G$OGSCfN'$,;H$($J$$$N$G(J
 | |$@$$$D$b(Jf$@$,B8:_$9$k$H$O8B$i$J$$$?$a$H$$$&$3$H$G$9!#(J
 | |
 | |$@%/%i%9$r=89g$HFI$_BX$($l$P!"F1$8$3$H$,$$(J$@$($k$G$7$g$&!#(J
 |
 |$@$($C!)(J
 |Boolean valued model $@$G$O$=$N(J f $@$r$+$-=8$a$F(J Universe $@$K$7$F$$$k$s$G$9(J
 |$@$h!#$=$N(J f $@$,B8:_$7$J$$!V$b$N!W$J$s$F$b$H$+$i4X78$J$$$N$G$O!#(J

model $@$r:n$k$H$-$KMQ$$$F$$$k%a%?M}O@$N(J$@Cf$G$O!"8EE5O@M}$r;H$C$F$^$9$+$i!"(J
characteristic function $@$O>o$K:n$l$k$N$G$9!#(J
$@$G$b!"D>4Q<g5AO@M}$N$b(J$@$H$G$O!"=89g$N(J characteristic function $@$O:n$l$k(J
$@$H$O8B$i$J$$$N$G$9!#(J

 | |$@$5$F!"<ALd$J$N$G$9$,(J
 | |$@&8(J$@$H$7$F0LAj6u4V$N3+=89g$NB+$r$H$k$H$7$^$9!#(J
 | |$@3+=89g$OM-8B2s$N6&DL=89g$HG$0U2s$NOB=89g$NA`:n$G3+=89g(J$@$N>r7o$rJ]$A$^$9$,(J
 | |$@$3$l$r;H$C$FLLGr$$Nc$r9M$($F$_$^$7$?!#(J
 | |$@Nc$($P(J
 | |Not(All x (P(x))) = 1
 | |$@$G(J
 | |Exist x (Not (P(x))) = 0
 | |$@$H$J$k$h$&$J(JP(x)$@$O<B:]$K$"$k$N$G$7$g$&$+!#(J
 |
 |$@$3$l$OA4A3OC$7$,(J$@D7$s$8$c$C$F(J $@&X(J-$@L5L7=b$NOC$7$G$O$J$$$G$7$g$&$+!#(J

\Omega $@L5L7=b$NOC$H$b$A$g$C$H0c$$$^$9$M!#(J

 | |$@$I$&(J$@$7$F>e$N$h$&$J$3$H$r;W$$IU$$$?$+$H$$$&$H(J
 | |$@>e$N<0$r&8$,(J[0,1]$@$H$7$F!"%b%G%k>e$G9M$($F(J
 | |x$@$,M-M}?t>e(J$@$rF0$-(J
 | ||P(x)|$@$,M-M}?t$r=|$$$?3+=89g$@$H$9$k$H!"(J
 |
 |$@$=$l3+=89g$K$J$k$s$G$9$+!)%6%j%9%-!<0LAj$@$H(J$@$7$?$iL58B$N@Q$G$9$h!#(J
 |
 |$@$H$$$&Lu$G;d$O$=$s$J(J P(x) $@$r4^$`$h$&$J=89gO@$N%b%G%k$OB8:_$7$J$$$H$_$?(J
 |$@$,!"$5$F!">.NS$5$s$+$i$N@52r$O!"!"!"(J

$@$=$&$$$&%b%G%k$O<B:]$K:n$l$^$9!#(J\Omega $@$r(J [0,1] $@$NDL>o$N0LAj$K$h(J$@$k3+=8(J
$@9g7O$H$7$F!"(JV^(\Omega) $@$r9M$($^$9!#(JV^(\Omega) $@$K$*$1$k(J($@%G%G%-%s%H%+%C(J
$@%H$K$h$k(J)$@<B?t$O!"(JV $@$K$*$1(J$@$k(J [0,1] $@$+$i(J R $@$X$NO"B34X?t$KBP1~$7$^$9!#$=(J
$@$3$G!"(J[0,1] $@>e$N(J identity function id$@$KBP1~$9$k(J V^(\Omega) $@$N<B?t(J id~ 
$@$r9M$(!"(JP(x) $@$O(J x < id~ or x > id~ $@$H$9$l$P$h$$$N$G$9!#(J
--
			$@N6C+Bg3XM}9)3XIt?tM}>pJs(J$@3X2J(J    $@>.NS(J  $@Ao(J
			satoshi@whale.ryukoku.ac.jp
			0775-43-7523($@3X2J;vL3<<(J) 0775-43-7528($@8&5f<<(J)
			0775-43-7524(FAX)
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Message-ID: <SATOSHI.92Nov30192259@whale.ryukoku.ac.jp>
Path: arc1-ca.pugleaf.net!sparky!uunet!ccut!sh.wide!wnoc-kyo!kuis!rins!satoshi
References: <526@keu02.rtri.or.jp> <RYU.92Nov14014631@sysipk.sys.titech.ac.jp> <530@keu02.rtri.or.jp> <RYU.92Nov17082028@sysipk.sys.titech.ac.jp> <544@keu02.rtri.or.jp> <SHINGO.92Nov27194549@ipc02.rtri.or.jp> <RYU.92Nov28090325@sysipk.sys.titech.ac.jp>

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Path: arc1-ca.pugleaf.net!sparky!uunet!ccut!sh.wide!wnoc-kyo!kuis!rins!satoshi
From: satoshi@whale.ryukoku.ac.jp (Satoshi Kobayashi)
Newsgroups: fj.sci.math
Subject: Re: Q in intuitionistic math.
Message-ID: <SATOSHI.92Nov30192259@whale.ryukoku.ac.jp>
Date: 30 Nov 92 10:22:59 GMT
References: <526@keu02.rtri.or.jp> <RYU.92Nov14014631@sysipk.sys.titech.ac.jp>
 <530@keu02.rtri.or.jp> <RYU.92Nov17082028@sysipk.sys.titech.ac.jp>
 <544@keu02.rtri.or.jp> <SHINGO.92Nov27194549@ipc02.rtri.or.jp>
 <RYU.92Nov28090325@sysipk.sys.titech.ac.jp>
Sender: news@rins.ryukoku.ac.jp
Distribution: fj
Organization: Ryukoku Univ., Seta, Japan
Lines: 59
In-reply-to: ryu@sys.titech.ac.jp's message of 28 Nov 92 00:03:25 GMT