On order-types of models of arithmetic - of PDMI RAS
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On order-types of models of arithmetic - of PDMI RAS
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On order-types of models of arithmetic by Andrey I. Bovykin
A thesis submitted to the University of Birmingham for the degree of Ph. D. in the Faculty of Science
School of Mathematics and Statistics, The University of Birmingham, Edgbaston, Birmingham, B15 2TT. 13 April, 2000
Synopsis In this thesis we study a range of questions related to the order structure of models of first-order Peano Arithmetic. In Chapter 1 we give necessary definitions and describe the current state of the subject in the literature survey. In Chapter 2 we study first properties of order-types of models of PA, give examples and place first restrictions on what the order-type of a model of PA can be. In Chapter 3 we study models generated by indiscernibles and prove that the model generated by a set of indiscernibles ordered as a dense linear order (C,
