Sh:924

• Shelah, S. (2015). Models of PA: when two elements are necessarily order automorphic. MLQ Math. Log. Q., 61(6), 399–417. arXiv: 1004.3342 DOI: 10.1002/malq.200920124 MR: 3433640
• Abstract:
  We are interested in the question of how much the order of a non-standard model of PA can determine the model. In particular, for a model M, we want to characterize the complete types p(x,y) of non-standard elements (a,b) such that the linear orders \{x:x< a\} and \{x:x < b\} are necessarily isomorphic. It is proved that this set includes the complete types p(x,y) such that if the pair (a,b) realizes it (in M) then there is an element c such that for all standard n,c^n < a,c^n < b,a < bc and b < ac. We prove that this is optimal, because if \diamondsuit_{\aleph_1} holds, then there is M of cardinality \aleph_1 for which we get equality. We also deal with how much the order in a model of PA may determine the addition.
• Version 2016-03-08_12 (27p) published version (19p)

@article{Sh:924,
 author = {Shelah, Saharon},
 title = {{Models of PA: when two elements are necessarily order automorphic}},
 journal = {MLQ Math. Log. Q.},
 fjournal = {MLQ. Mathematical Logic Quarterly},
 volume = {61},
 number = {6},
 year = {2015},
 pages = {399--417},
 issn = {0942-5616},
 mrnumber = {3433640},
 mrclass = {03C62 (03C64 03E65 03H15)},
 doi = {10.1002/malq.200920124},
 note = {\href{https://arxiv.org/abs/1004.3342}{arXiv: 1004.3342}},
 arxiv_number = {1004.3342}
}