Unit:
Κατεύθυνση Αλγόριθμοι, Λογική και Διακριτά Μαθηματικά (Α.Λ.ΜΑ.)Πληροφορική
Author:
Apostolou Filippos
Supervisors info:
Σουλδάτος Ιωάννης, Επίκουρος Καθηγητής, Τμήμα Μαθηματικών, Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης.
Ροντογιάννης Παναγιώτης, Καθηγητής, Τμήμα Πληροφορικής και Τηλεπικοινωνιών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών.
Original Title:
Morley’s Categoricity Theorem
Translated title:
Morley’s Categoricity Theorem
Summary:
Morley’s categoricity theorem stands as a cornerstone in model theory, with many experts considering it the beginning of modern model theory. A complete theory T in a countable language is κ-categorical if it has a unique (up to isomorphism) model of cardinality κ. Morley, with his PhD thesis ”Categoricity in Power”, published in 1962, positively answered the conjecture of Łoś stating that if T is κ-categorical for some uncountable κ, then it is κ-categorical for any uncountable κ. This theorem is now known as the categoricity theorem. The ideas used to prove it now play a central role in model theory and still shape the direction of the field. We will follow a recent proof given by Lachlan and Baldwin, which presents many ideas and definitions that are still at the forefront of research, the way it is presented in ” Model Theory: An Introduction” by David Marker.
Main subject category:
Science
Keywords:
Uncountably Categorical Theory, Algebraic Closure, Type
