Extendible sets in peano arithmetic

Stuart T. Smith

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Let A be a structure and let U be a subset of \A\. We say U is extendible if whenever B is an elementary extension of A.there is a V ⊆B\ such that (A, U) < (B, V). Our main results are: If Jt is a countable model of Peano arithmetic and U is a subset of M, then U is extendible iff U is parametrically definable in M. Also, the cofinally extendible subsets of \M\ are exactly the inductive subsets of \M\. The end extendible subsets of \M\ are not completely characterized, but we show that if N is a model of Peano arithmetic of arbitrary cardinality and U is any bounded subset of jr", then U is end extendible.

Original languageEnglish
Pages (from-to)337-367
Number of pages31
JournalTransactions of the American Mathematical Society
Issue number1
StatePublished - 1 Jan 1989

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics


Dive into the research topics of 'Extendible sets in peano arithmetic'. Together they form a unique fingerprint.

Cite this