- [[Formal System]] - [[Completeness]] - [[Consistent]] - [[Godel's First Incompleteness Theorem]] - [[Godel's Second Incompleteness Theorem]] - in the trival case of an [[Consistent|Inconsistent]] [[Formal System]], the system is always [[Completeness|Complete]] - since literally any statement can be proven - so we only care about [[Consistent]] systems that we actually use https://plato.stanford.edu/entries/goedel-incompleteness/#:~:text=A%20formal%20system%20is%20complete,both%20derivable%20in%20the%20system https://www.quantamagazine.org/how-godels-proof-works-20200714/ https://www.youtube.com/watch?v=HeQX2HjkcNo&t=1237s