@incollection{VAUGHT196614,
    Abstract = {Publisher Summary This introductory chapter discusses the general method for establishing the undecidability of theories. The chapter presents a new proof of Cobham's theorem that may be called as ``existential interpretation.'' Cobham's theorem can be derived from a theorem of Traht{\'e}nbrot. The chapter also discusses several other ways in which Cobham's theorem can be improved or generalized along with a new proof of Cobham's theorem. Any axiomatizable theory whose undecidability follows from Traht{\'e}nbrots theorem also fulfills the hypothesis of Tarski's condition. The chapter shows a way to proof that the similar conclusion also applies to axiomatizable theories whose undecidability follows from Cobham's Theorem. Cobham proves the theory of groups (G) of finite groups in hereditarily and undecidable manner (and, hence, not axiomatizable).The chapter also illustrates several related problems to Cobham's theorem.},
    Author = {Vaught, Robertl.},
    BookTitle = {Logic, Methodology and Philosophy of Science},
    Editor = {Nagel, Ernest and Suppes, Patrick and Tarski, Alfred},
    File = {On a Theorem of Cobham Concerning Undecidable Theories - vaught1966.pdf},
    ISSN = {0049-237X},
    Pages = {14-25},
    Publisher = {Elsevier},
    Series = {Studies in Logic and the Foundations of Mathematics},
    Title = {On a Theorem of Cobham Concerning Undecidable Theories},
    URL = {https://www.sciencedirect.com/science/article/pii/S0049237X0970566X},
    Volume = {44},
    Year = {1966},
    bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0049237X0970566X},
    bdsk-url-2 = {https://doi.org/10.1016/S0049-237X(09)70566-X},
    date-added = {2021-09-07 11:54:20 +0200},
    date-modified = {2021-09-07 11:54:20 +0200},
    doi = {10.1016/S0049-237X(09)70566-X}
}

@incollection{VAUGHT196614, Abstract = {Publisher Summary This introductory chapter discusses the general method for establishing the undecidability of theories. The chapter presents a new proof of Cobham's theorem that may be called as ``existential interpretation.'' Cobham's theorem can be derived from a theorem of Traht{\'e}nbrot. The chapter also discusses several other ways in which Cobham's theorem can be improved or generalized along with a new proof of Cobham's theorem. Any axiomatizable theory whose undecidability follows from Traht{\'e}nbrots theorem also fulfills the hypothesis of Tarski's condition. The chapter shows a way to proof that the similar conclusion also applies to axiomatizable theories whose undecidability follows from Cobham's Theorem. Cobham proves the theory of groups (G) of finite groups in hereditarily and undecidable manner (and, hence, not axiomatizable).The chapter also illustrates several related problems to Cobham's theorem.}, Author = {Vaught, Robertl.}, BookTitle = {Logic, Methodology and Philosophy of Science}, Editor = {Nagel, Ernest and Suppes, Patrick and Tarski, Alfred}, File = {On a Theorem of Cobham Concerning Undecidable Theories - vaught1966.pdf}, ISSN = {0049-237X}, Pages = {14-25}, Publisher = {Elsevier}, Series = {Studies in Logic and the Foundations of Mathematics}, Title = {On a Theorem of Cobham Concerning Undecidable Theories}, URL = {https://www.sciencedirect.com/science/article/pii/S0049237X0970566X}, Volume = {44}, Year = {1966}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0049237X0970566X}, bdsk-url-2 = {https://doi.org/10.1016/S0049-237X(09)70566-X}, date-added = {2021-09-07 11:54:20 +0200}, date-modified = {2021-09-07 11:54:20 +0200}, doi = {10.1016/S0049-237X(09)70566-X} }