. . "In mathematics, Hilbert's second problem was posed by David Hilbert in 1900 as one of his 23 problems. It asks for a proof that the arithmetic is consistent \u2013 free of any internal contradictions. Hilbert stated that the axioms he considered for arithmetic were the ones given in , which include a second order completeness axiom. In the 1930s, Kurt G\u00F6del and Gerhard Gentzen proved results that cast new light on the problem. Some feel that G\u00F6del's theorems give a negative solution to the problem, while others consider Gentzen's proof as a partial positive solution."@en . . . . . "Hilberts andra problem \u00E4r ett av David Hilbert 23 matematiska problem. Det formulerades \u00E5r 1900. Hypotesen \u00E4r att aritmetikens axiom \u00E4r konsistenta, det vill s\u00E4ga att aritmetik \u00E4r ett formellt system utan mots\u00E4gelser. Problemet \u00E4r delvis l\u00F6st. Vissa anser att det har bevisats vara om\u00F6jligt att bevisa avsaknad av mots\u00E4gelser i ett axiomatiskt system med en \u00E4ndlig m\u00E4ngd axiom. Se G\u00F6dels ofullst\u00E4ndighetsteorem."@sv . "\u5E0C\u723E\u4F2F\u7279\u7B2C\u4E8C\u554F\u984C\uFF0C\u662F\u5E0C\u723E\u4F2F\u7279\u768423\u500B\u554F\u984C\u4E4B\u4E00\uFF0C\u5373\u95DC\u65BC\u4E00\u500B\u516C\u7406\u7CFB\u7D71\u76F8\u5BB9\u6027\u7684\u554F\u984C\uFF0C\u4E5F\u5C31\u662F\u5224\u5B9A\u4E00\u500B\u516C\u7406\u7CFB\u7D71\u5167\u7684\u6240\u547D\u984C\u662F\u5F7C\u6B64\u7121\u77DB\u76FE\u7684\uFF0C\u5E0C\u723E\u4F2F\u7279\u5E0C\u671B\u80FD\u4EE5\u56B4\u8B39\u7684\u65B9\u5F0F\u4F86\u8B49\u660E\u4EFB\u610F\u516C\u7406\u7CFB\u7D71\u5167\u547D\u984C\u7684\u76F8\u5BB9\u6027\u3002 \u5967\u5730\u5229\u6578\u5B78\u5BB6\u5E93\u5C14\u7279\u00B7\u54E5\u5FB7\u5C14\uFF08Kurt Friedrich G\u00F6del\uFF09\u57281930\u5E74\u8B49\u660E\u4E86\u54E5\u5FB7\u5C14\u4E0D\u5B8C\u5907\u5B9A\u7406\uFF08G\u00F6del's incompleteness theorems\uFF09\uFF0C\u7C89\u788E\u4E86\u5E0C\u723E\u4F2F\u7279\u7684\u5922\u60F3\u3002"@zh . . . "Segundo problema de Hilbert"@pt . . . . . . . "Hilberts zweites Problem"@de . "\u0412\u0442\u043E\u0440\u0430\u044F \u043F\u0440\u043E\u0431\u043B\u0435\u043C\u0430 \u0413\u0438\u043B\u044C\u0431\u0435\u0440\u0442\u0430 \u0438\u0437 \u0437\u043D\u0430\u043C\u0435\u043D\u0438\u0442\u044B\u0445 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u0435\u0441\u043A\u0438\u0445 \u043F\u0440\u043E\u0431\u043B\u0435\u043C, \u043A\u043E\u0442\u043E\u0440\u044B\u0435 \u0414\u0430\u0432\u0438\u0434 \u0413\u0438\u043B\u044C\u0431\u0435\u0440\u0442 \u0432\u044B\u0434\u0432\u0438\u043D\u0443\u043B \u0432 1900 \u0433\u043E\u0434\u0443 \u0432 \u041F\u0430\u0440\u0438\u0436\u0435 \u043D\u0430 II \u041C\u0435\u0436\u0434\u0443\u043D\u0430\u0440\u043E\u0434\u043D\u043E\u043C \u041A\u043E\u043D\u0433\u0440\u0435\u0441\u0441\u0435 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u043E\u0432. \u0414\u043E \u0441\u0438\u0445 \u043F\u043E\u0440 \u0441\u0440\u0435\u0434\u0438 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u0435\u0441\u043A\u043E\u0433\u043E \u0441\u043E\u043E\u0431\u0449\u0435\u0441\u0442\u0432\u0430 \u043D\u0435\u0442 \u043A\u043E\u043D\u0441\u0435\u043D\u0441\u0443\u0441\u0430 \u043E\u0442\u043D\u043E\u0441\u0438\u0442\u0435\u043B\u044C\u043D\u043E \u0442\u043E\u0433\u043E, \u0440\u0435\u0448\u0435\u043D\u0430 \u043E\u043D\u0430 \u0438\u043B\u0438 \u043D\u0435\u0442. \u041F\u0440\u043E\u0431\u043B\u0435\u043C\u0430 \u0437\u0432\u0443\u0447\u0438\u0442 \u0442\u0430\u043A: \u043F\u0440\u043E\u0442\u0438\u0432\u043E\u0440\u0435\u0447\u0438\u0432\u044B \u0438\u043B\u0438 \u043D\u0435\u0442 \u0430\u043A\u0441\u0438\u043E\u043C\u044B \u0430\u0440\u0438\u0444\u043C\u0435\u0442\u0438\u043A\u0438? \u041A\u0443\u0440\u0442 \u0413\u0451\u0434\u0435\u043B\u044C \u0434\u043E\u043A\u0430\u0437\u0430\u043B, \u0447\u0442\u043E \u043D\u0435\u043F\u0440\u043E\u0442\u0438\u0432\u043E\u0440\u0435\u0447\u0438\u0432\u043E\u0441\u0442\u044C \u0430\u043A\u0441\u0438\u043E\u043C \u0430\u0440\u0438\u0444\u043C\u0435\u0442\u0438\u043A\u0438 \u043D\u0435\u043B\u044C\u0437\u044F \u0434\u043E\u043A\u0430\u0437\u0430\u0442\u044C, \u0438\u0441\u0445\u043E\u0434\u044F \u0438\u0437 \u0441\u0430\u043C\u0438\u0445 \u0430\u043A\u0441\u0438\u043E\u043C \u0430\u0440\u0438\u0444\u043C\u0435\u0442\u0438\u043A\u0438 (\u0435\u0441\u043B\u0438 \u0442\u043E\u043B\u044C\u043A\u043E \u0430\u0440\u0438\u0444\u043C\u0435\u0442\u0438\u043A\u0430 \u043D\u0435 \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u043D\u0430 \u0441\u0430\u043C\u043E\u043C \u0434\u0435\u043B\u0435 \u043F\u0440\u043E\u0442\u0438\u0432\u043E\u0440\u0435\u0447\u0438\u0432\u043E\u0439). \u041A\u0440\u043E\u043C\u0435 \u0413\u0451\u0434\u0435\u043B\u044F, \u043C\u043D\u043E\u0433\u0438\u0435 \u0434\u0440\u0443\u0433\u0438\u0435 \u0432\u044B\u0434\u0430\u044E\u0449\u0438\u0435\u0441\u044F \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438 \u0437\u0430\u043D\u0438\u043C\u0430\u043B\u0438\u0441\u044C \u044D\u0442\u043E\u0439 \u043F\u0440\u043E\u0431\u043B\u0435\u043C\u043E\u0439."@ru . . . . . . . . . . . . "Na matem\u00E1tica, o segundo problema de Hilbert foi proposto por David Hilbert em 1900, sendo esse um dos seus 23 problemas. Esse problema consiste em provar que a aritm\u00E9tica \u00E9 consistente - livre de qualquer contradi\u00E7\u00E3o interna.No anos de 1930, Kurt G\u00F6del e Gerhard Gentzen provaram resultados que voltaram a chamar aten\u00E7\u00E3o para esse problema. Alguns acham que esses resultados resolveram o problema, enquanto outros acham que ele ainda est\u00E1 em aberto."@pt . "\u5E0C\u723E\u4F2F\u7279\u7B2C\u4E8C\u554F\u984C"@zh . . . "Hilberts andra problem"@sv . . . "La cuesti\u00F3n de la compatibilidad de los axiomas de la aritm\u00E9tica, tambi\u00E9n conocida como segundo problema de Hilbert (uno de los 23 problemas expuestos en 1900 por el matem\u00E1tico alem\u00E1n David Hilbert), se\u00F1ala la importancia y la necesidad de formalizar la matem\u00E1tica. Esta inquietud nace a partir de la incertidumbre que se gener\u00F3 al hacer deducciones sobre axiomas que no son tan evidentes como podr\u00EDan parecer a primera vista, y en este punto se hace notar el contraste de las matem\u00E1ticas con la geometr\u00EDa, donde los axiomas son de alg\u00FAn modo visibles como es el caso de los postulados de Euclides."@es . . . . . . "152759"^^ . . . . . . "La cuesti\u00F3n de la compatibilidad de los axiomas de la aritm\u00E9tica, tambi\u00E9n conocida como segundo problema de Hilbert (uno de los 23 problemas expuestos en 1900 por el matem\u00E1tico alem\u00E1n David Hilbert), se\u00F1ala la importancia y la necesidad de formalizar la matem\u00E1tica. Esta inquietud nace a partir de la incertidumbre que se gener\u00F3 al hacer deducciones sobre axiomas que no son tan evidentes como podr\u00EDan parecer a primera vista, y en este punto se hace notar el contraste de las matem\u00E1ticas con la geometr\u00EDa, donde los axiomas son de alg\u00FAn modo visibles como es el caso de los postulados de Euclides."@es . . . . . . . "\u5E0C\u723E\u4F2F\u7279\u7B2C\u4E8C\u554F\u984C\uFF0C\u662F\u5E0C\u723E\u4F2F\u7279\u768423\u500B\u554F\u984C\u4E4B\u4E00\uFF0C\u5373\u95DC\u65BC\u4E00\u500B\u516C\u7406\u7CFB\u7D71\u76F8\u5BB9\u6027\u7684\u554F\u984C\uFF0C\u4E5F\u5C31\u662F\u5224\u5B9A\u4E00\u500B\u516C\u7406\u7CFB\u7D71\u5167\u7684\u6240\u547D\u984C\u662F\u5F7C\u6B64\u7121\u77DB\u76FE\u7684\uFF0C\u5E0C\u723E\u4F2F\u7279\u5E0C\u671B\u80FD\u4EE5\u56B4\u8B39\u7684\u65B9\u5F0F\u4F86\u8B49\u660E\u4EFB\u610F\u516C\u7406\u7CFB\u7D71\u5167\u547D\u984C\u7684\u76F8\u5BB9\u6027\u3002 \u5967\u5730\u5229\u6578\u5B78\u5BB6\u5E93\u5C14\u7279\u00B7\u54E5\u5FB7\u5C14\uFF08Kurt Friedrich G\u00F6del\uFF09\u57281930\u5E74\u8B49\u660E\u4E86\u54E5\u5FB7\u5C14\u4E0D\u5B8C\u5907\u5B9A\u7406\uFF08G\u00F6del's incompleteness theorems\uFF09\uFF0C\u7C89\u788E\u4E86\u5E0C\u723E\u4F2F\u7279\u7684\u5922\u60F3\u3002"@zh . . . . "13024"^^ . "In mathematics, Hilbert's second problem was posed by David Hilbert in 1900 as one of his 23 problems. It asks for a proof that the arithmetic is consistent \u2013 free of any internal contradictions. Hilbert stated that the axioms he considered for arithmetic were the ones given in , which include a second order completeness axiom. In the 1930s, Kurt G\u00F6del and Gerhard Gentzen proved results that cast new light on the problem. Some feel that G\u00F6del's theorems give a negative solution to the problem, while others consider Gentzen's proof as a partial positive solution."@en . . "\u0412\u0442\u043E\u0440\u0430\u044F \u043F\u0440\u043E\u0431\u043B\u0435\u043C\u0430 \u0413\u0438\u043B\u044C\u0431\u0435\u0440\u0442\u0430"@ru . . . . . . "Hilberts andra problem \u00E4r ett av David Hilbert 23 matematiska problem. Det formulerades \u00E5r 1900. Hypotesen \u00E4r att aritmetikens axiom \u00E4r konsistenta, det vill s\u00E4ga att aritmetik \u00E4r ett formellt system utan mots\u00E4gelser. Problemet \u00E4r delvis l\u00F6st. Vissa anser att det har bevisats vara om\u00F6jligt att bevisa avsaknad av mots\u00E4gelser i ett axiomatiskt system med en \u00E4ndlig m\u00E4ngd axiom. Se G\u00F6dels ofullst\u00E4ndighetsteorem."@sv . "1106495612"^^ . "Hilbert's second problem"@en . . . "Compatibilidad de los axiomas de la aritm\u00E9tica"@es . . "Na matem\u00E1tica, o segundo problema de Hilbert foi proposto por David Hilbert em 1900, sendo esse um dos seus 23 problemas. Esse problema consiste em provar que a aritm\u00E9tica \u00E9 consistente - livre de qualquer contradi\u00E7\u00E3o interna.No anos de 1930, Kurt G\u00F6del e Gerhard Gentzen provaram resultados que voltaram a chamar aten\u00E7\u00E3o para esse problema. Alguns acham que esses resultados resolveram o problema, enquanto outros acham que ele ainda est\u00E1 em aberto."@pt . . . . . . . . "\u0412\u0442\u043E\u0440\u0430\u044F \u043F\u0440\u043E\u0431\u043B\u0435\u043C\u0430 \u0413\u0438\u043B\u044C\u0431\u0435\u0440\u0442\u0430 \u0438\u0437 \u0437\u043D\u0430\u043C\u0435\u043D\u0438\u0442\u044B\u0445 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u0435\u0441\u043A\u0438\u0445 \u043F\u0440\u043E\u0431\u043B\u0435\u043C, \u043A\u043E\u0442\u043E\u0440\u044B\u0435 \u0414\u0430\u0432\u0438\u0434 \u0413\u0438\u043B\u044C\u0431\u0435\u0440\u0442 \u0432\u044B\u0434\u0432\u0438\u043D\u0443\u043B \u0432 1900 \u0433\u043E\u0434\u0443 \u0432 \u041F\u0430\u0440\u0438\u0436\u0435 \u043D\u0430 II \u041C\u0435\u0436\u0434\u0443\u043D\u0430\u0440\u043E\u0434\u043D\u043E\u043C \u041A\u043E\u043D\u0433\u0440\u0435\u0441\u0441\u0435 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u043E\u0432. \u0414\u043E \u0441\u0438\u0445 \u043F\u043E\u0440 \u0441\u0440\u0435\u0434\u0438 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u0435\u0441\u043A\u043E\u0433\u043E \u0441\u043E\u043E\u0431\u0449\u0435\u0441\u0442\u0432\u0430 \u043D\u0435\u0442 \u043A\u043E\u043D\u0441\u0435\u043D\u0441\u0443\u0441\u0430 \u043E\u0442\u043D\u043E\u0441\u0438\u0442\u0435\u043B\u044C\u043D\u043E \u0442\u043E\u0433\u043E, \u0440\u0435\u0448\u0435\u043D\u0430 \u043E\u043D\u0430 \u0438\u043B\u0438 \u043D\u0435\u0442. \u041F\u0440\u043E\u0431\u043B\u0435\u043C\u0430 \u0437\u0432\u0443\u0447\u0438\u0442 \u0442\u0430\u043A: \u043F\u0440\u043E\u0442\u0438\u0432\u043E\u0440\u0435\u0447\u0438\u0432\u044B \u0438\u043B\u0438 \u043D\u0435\u0442 \u0430\u043A\u0441\u0438\u043E\u043C\u044B \u0430\u0440\u0438\u0444\u043C\u0435\u0442\u0438\u043A\u0438? \u041A\u0443\u0440\u0442 \u0413\u0451\u0434\u0435\u043B\u044C \u0434\u043E\u043A\u0430\u0437\u0430\u043B, \u0447\u0442\u043E \u043D\u0435\u043F\u0440\u043E\u0442\u0438\u0432\u043E\u0440\u0435\u0447\u0438\u0432\u043E\u0441\u0442\u044C \u0430\u043A\u0441\u0438\u043E\u043C \u0430\u0440\u0438\u0444\u043C\u0435\u0442\u0438\u043A\u0438 \u043D\u0435\u043B\u044C\u0437\u044F \u0434\u043E\u043A\u0430\u0437\u0430\u0442\u044C, \u0438\u0441\u0445\u043E\u0434\u044F \u0438\u0437 \u0441\u0430\u043C\u0438\u0445 \u0430\u043A\u0441\u0438\u043E\u043C \u0430\u0440\u0438\u0444\u043C\u0435\u0442\u0438\u043A\u0438 (\u0435\u0441\u043B\u0438 \u0442\u043E\u043B\u044C\u043A\u043E \u0430\u0440\u0438\u0444\u043C\u0435\u0442\u0438\u043A\u0430 \u043D\u0435 \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u043D\u0430 \u0441\u0430\u043C\u043E\u043C \u0434\u0435\u043B\u0435 \u043F\u0440\u043E\u0442\u0438\u0432\u043E\u0440\u0435\u0447\u0438\u0432\u043E\u0439). \u041A\u0440\u043E\u043C\u0435 \u0413\u0451\u0434\u0435\u043B\u044F, \u043C\u043D\u043E\u0433\u0438\u0435 \u0434\u0440\u0443\u0433\u0438\u0435 \u0432\u044B\u0434\u0430\u044E\u0449\u0438\u0435\u0441\u044F \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438 \u0437\u0430\u043D\u0438\u043C\u0430\u043B\u0438\u0441\u044C \u044D\u0442\u043E\u0439 \u043F\u0440\u043E\u0431\u043B\u0435\u043C\u043E\u0439."@ru . . .