GILBERT AKSIOMALAR SISTEMASIDA IZCHILLIK VA TO‘LIQLIK MASALALARI
Ключевые слова:
Gilbert aksiomalari, izchillik, to‘liqlik, aksiomatik sistema, geometriya asoslari, formal tizim, mantiq, model, mustaqillik, Evklid geometriyasi.Аннотация
Ushbu maqolada David Gilbert tomonidan ishlab chiqilgan aksiomatik geometriya sistemasida izchillik va to‘liqlik masalalari o‘rganiladi. Natijalarda Gilbert aksiomalar sistemasining izchilligi Evklid geometriyasi modeli orqali asoslandi, to‘liqlik tushunchasi esa barcha geometriya teoremalarini chiqarish imkoniyati sifatida tavsiflandi. Shuningdek, ayrim aksiomalarning mustaqilligi misollar orqali ko‘rsatildi. Muhokama qismida olingan natijalar Kurt Gödel ning to‘liqlik va noto‘liqlik teoremalari bilan bog‘liq holda tahlil qilindi. Xulosa sifatida aksiomatik tizimlarning izchilligi va to‘liqligi matematik nazariyalarning asosiy mantiqiy mezonlari ekanligi ko‘rsatildi.
Библиографические ссылки
David Gilbert. Grundlagen der Geometrie (Geometriya asoslari). – Leipzig: Teubner, 1899.
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