Skip to main content
Article thumbnail
Location of Repository

Initial segments and end-extensions of models of arithmetic

By Tin Lok Wong

Abstract

This thesis is organized into two independent parts. In the first part, we extend the recent work on generic cuts by Kaye and the author. The focus here is the properties of the pairs (M, I) where I is a generic cut of a model M. Amongst other results, we characterize the theory of such pairs, and prove that they are existentially closed in a natural category. In the second part, we construct end-extensions of models of arithmetic that are at least as strong as ATR\(_0\). Two new constructions are presented. The first one uses a variant of Fodor’s Lemma in ATR\(_0\) to build an internally rather classless model. The second one uses some weak versions of the Galvin–Prikry Theorem in adjoining an ideal set to a model of second-order arithmetic

Topics: QA Mathematics
Year: 2010
OAI identifier: oai:etheses.bham.ac.uk:884

Suggested articles

Citations

  1. (2003). Anand Pillay, and Evgueni Vassiliev. Lovely pairs of models. doi
  2. (2007). Bounding homogeneous models. doi
  3. (2004). Bounding prime models. doi
  4. If (heaven forbid) the fraternity of non-Riemannian hypersquarers should ever die out, our hero’s writings would become less translatable than those of the Maya. Philip J. Davis and Reuben Hersh The Mathematical Experience [8], on the Ideal Mathematician
  5. (1977). Model Theory,
  6. (2001). On end extensions of models of subsystems of Peano arithmetic. doi
  7. (2008). On two problems concerning end-extensions. doi
  8. (1966). Set Theory and the Continuum Hypothesis. doi
  9. (2005). Subsets of superstable structures are weakly benign. doi
  10. (1981). The Mathematical Experience. Birkha¨user,

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.