# Umsebenzi wobugcisa kaThixo1220

Xa uKurt Gödel wapapasha iTheorems yakhe edumileyo yokungazaliseki ngo-1931, yagungqisa iziseko zengqondo yemathematika: Waphikisa ukuba zonke ii-axioms ezinokusekwa njengesiseko ezinokwenzeka ngokuqinisekileyo azigqibekanga ukuze zingqine zonke iingxelo ngamanani-kwaye wayitshabalalisa loo nto Iphupha likaHilbert lokungqina ukungqinelana kwethiyori yezibalo.

Ukungeniswa kwamanani eGödel (imephu yefomula engacacanga kumanani endalo) kunye nokwahlula-hlula (ukutshintshwa kwesitshintshi simahla kwimisebenzi kunye nenombolo yabo ye-Gödel) zizinto ezimbini eziphambili ezaziswa nguGödel kubungqina bakhe. Umbono wobungqina obuchazayo apho iGödel idibanisa khona la magama angabhalwa ngolu hlobo lulandelayo:

$$P(p) \, \text{wahr} \Leftrightarrow p \in \, \overline{B}^* \Leftrightarrow d(p) \in \overline{B} \Leftrightarrow d(p) \notin B \Leftrightarrow g(P(p)) \notin B \Leftrightarrow P(p) \, \text{unbeweisbar}$$

Kuba $$P(p)$$ ayinakuba yinyani (kuba ibinokuchaphazeleka kwaye ke iyinyani), $$P(p)$$ yinyani kwaye ke ayizukubakho. Ke kuhlala kukho isigwebo esiyinyani kulwimi (kunye naluphi na ukhetho lwee-axioms) ezingenakubonakaliswa. Apha $$g$$ i Gödelization, $$p$$ i Gödel inani isivisa $$P$$ , nto leyo archetype edibanayo $$\overline{B}^*$$ of $$B$$ (i isethi yonke Amanani e-Godel azo zonke izindululo ezinokubakho) phantsi komsebenzi wokudibanisa $$d$$ .

Ukuqhubeka kokufunda sicebisa ukupapashwa kukaGödel ngo-1931 kunye nenqaku elifundwe kakuhle nguStepan Parunashvili . Ukongeza kwiithiyori zokungagqitywa, uGödel wenze ezinye izinto eziphumelelayo, kubandakanya ukungabinakuphikiswa kweCantor's continuum hypothesis kunye nobungqina be - ontological kaThixo kulwimi lwendlela yokucinga.

Emva