Joosten, Joost J.Papafilippou, Konstantinos2020-09-212020-09-212020-09https://hdl.handle.net/2445/170755Treballs Finals del Màster de Lògica Pura i Aplicada, Facultat de Filosofia, Universitat de Barcelona, Curs: 2019-2020, Tutor: Joost J. JoostenIn this thesis we study Beklemishev’s combinatorial principle Every Worm Dies, EWD which although true, it is unprovable in Peano Arithmetic (PA). The principle talks about sequences of modal formulas, the finiteness of all of them being equivalent to the one-consistency of PA. We present the elements of proof theory at play here and perform two attempts at generalizing this theorem. One is directed towards its relationship with some known fragments of PA while the other aims to see its connection with fragments of second order arithmetic.66 p.application/pdfengcc by-nc-nd (c) Papafilippou, Konstantinos, 2020http://creativecommons.org/licenses/by-nc-nd/3.0/es/Lògica matemàticaAritmèticaTreballs de fi de màsterMathematical logicArithmeticMaster's thesesinfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccess