Carro Viqueira, Álvaro2026-05-182026-05-182024-07https://hdl.handle.net/10347/4725060 páxsOs teoremas da incompletude de Gödel, formulados polo lóxico austríaco Kurt Gödel en 1931, tiveron un impacto revolucionario na matemática e na filosofía. O primeiro establece que en calquera sistema lóxico suficientemente potente como para incluír á aritmética dos números naturais, habería sempre enunciados verdadeiros mais non demostrables dentro dese sistema. O segundo nega a posibilidade de probar a súa propia consistencia. Neste traballo abordarase o estudo dos sistemas lóxicos, que son marcos formais nos que se poden expresar axiomas e demostrar teoremas. Probarase a completude de certos destes sistemas para posteriormente estudar a aritmética común, co obxectivo último de demostrar ambos teoremas da incompletude.Gödel’s incompleteness theorems, formulated by the Austrian logician Kurt Gödel in 1931, had a revolutionary impact on mathematics and philosophy. The first establishes that in any sufficiently powerful logical system to include the arithmetic of natural numbers, there will always be true statements that cannot be proven within that system. The second denies the possibility of proving its own consistency. In this work, we will address the study of logical systems, which are formal frameworks in which axioms can be expressed and theorems be proven. We will show completeness in certain of these systems in order to study ordinary arithmetic, with the ultimate goal of proving both incompleteness theorems.glgAttribution-NonCommercial-ShareAlike 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-sa/4.0/bachelor thesisopen access