
tarsky-grothendic sanch siddhant

tarsky-grothendic sanch siddhant (tii. jee., ganitshastradnya alfried tarsky aanee alekzandar grothendic yanchya navavarun naav denyat aale) haah eka svayamsiddha sanch siddhant aahe. haah zarmelo-frankel sanch siddhantacha (zed. eff. see.) gair-snrakshak vistar aahe aanee tarskeechya svayamsiddhatechya samaveshadvare itar svayamsiddha sanch siddhantanpasun vegala aahe, jyamadhye asey mhatale aahe qee pratyek sanchasathi eka grauthendic vishva aahe jeey tyache aahe (khalee pahaa). tarskeecha svayamsiddha siddhant durgam cardinalsche astitva soochit karato, jeey zed. eff. see. peksha samruddha ontology pradan karato. udaharanarth, haah svayamsiddha siddhant jodane shreni siddhantala samarthan dete.
mizar pranali aanee metamath puravyanchya aupcharik padtalanisathi tarsky-grothendic sanch siddhant vapartat.
svayamsiddha.
tarsky-grothendic sanch siddhant paramparik zarmelo-frankel sanch siddhantapasun suru hoto aanee nantar "tarskeecha svayamsiddha siddhant" jodato. tyache varnan karnyasathi aapan mizarche svayamsiddha shabd, vyakhya aanee sanketan vaparu. mizarchya moolbhut vastoo aanee prakriya purnapane aupcharik aahet; tyanche anaupacharik varnan khalee dile aahe. pratham, aapan asey gruheet dharuyah
tii. jee. madhye khaleel svayamsiddha shabdancha samavesh aahe, jeey paramparik aahet kaaran teey dekhil zed. eff. see. chaa bhag aaheth
heey tarskyche svayamsiddha tatva aahe jeey tii. jee. laa itar svayamsiddha sanch siddhantanpasun vegale karate. tarskeecha svayamsiddha siddhant anant, nivad aanee shakti sanch yanche svayamsiddha siddhant dekhil soochit karato. heey durgam cardinalsche astitva dekhil soochit karate, jyamule tii. jee. chey ontology zed. eff. see. sarkhya paramparik sanch siddhantanpeksha barech samruddha aahe.
- sootra _ 7 swatach;
- sootra _ 10 chya pratyek sadasyacha pratyek ghatak;
- sootra _ 10 chya pratyek sadasyacha pratyek upasanch;
- sootra _ 10 chya pratyek sadasyacha shakti sanch;
- sootra 10 chaa pratyek upasanch sootra 10 peksha qamee aahe.
adhik aupcharikah
jethe "sootra _ 18" heey "x" chaa shakti varg darshavate aanee "sootra _ 19" heey samsankhya darshavate. (sthanik bhashet) tarskeecha swasiddhavakya asey sangato qee pratyek sanch sutrasathi _ 7 heey eka grauthendic vishva aahe jyache teey sambandhit aahe.
teey sootra _ 10 heey sootra _ 7 sathichya "sarvatrik sanch" sarkhe disate-tyat keval sadasya mhanoon sootra _ 7 chaa powerset aanee sootra _ 7 chey serve upasanch nasatat, tarr tyat tyaa powersetcha powerset dekhil asato aanee asech-tyache sadasya powerset ghenyachya kinwa upasanch ghenyachya karyantargat bund asatat. heey eka 'sarvatrik sanch' sarkhe aahe, parantu arthat too swatacha sadasya nahee aanee serve sanchancha sanch nahee. teey jyaa grauthendic vishvache aahe, tyachi khatri aahe. aanee mug asey konatehi sootra _ 10 swatach aanakhi mothya "jawaljawal sarvatrik sanch" chaa sadasya aahe. samanyatah astitvat asalyache gruheet dharalya jaananya ekapeksha mothya pramanat adhik sanchanchi hummy denanya majboot cardinality svayamsiddhinpaiki heey eka aahe.
mizar pranalimadhye amalbajavani.
tii. jee. chya amalbajavanimadhye aanee tyacha tarkik vakyarachana pradan karnyat antarbhut asaleli mizar bhasha type kelee jaate aanee prakar rikt nasalele manale jaatat. tyamule, haah siddhant apratyakshapane rikt nahee asey manale jaate. astitva svayamsiddha, eae.jee. aniyantrit jodiche astitva, constructor yaa sandnyechya vyakhyedvare apratyakshapane dekhil lagoo kele jaate.
yaa pranalimadhye samanata, sadasyatvacha andaj aanee khaleel manak vyakhya samavisht aaheth
metamathmadhye amalbajavani.
metamath pranali aniyantrit uchch-kram tarkshastrala samarthan dete, parantu tee samanyatah 'sanch' saha vaparali jaate.emm. emm.'. svayamsiddhanchya vyakhya. kuhwad-vaadh svayamsiddha sutramadhye tarskeecha svayamsiddha sootra jodala jaato, jyachi vyakhya metamathmadhye khalilpramane kelee aaheh
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