已收录 273081 条政策
 政策提纲
  • 暂无提纲
On groups and initial segments in nonstandard models of Peano Arithmetic
[摘要] This thesis concerns M-finite groups and a notion of discrete measure in models of Peano Arithmetic. First we look at a measure construction for arbitrary non-M-finite sets via suprema and infima of appropriate M-finite sets. The basic properties of the measures are covered, along with non-measurable sets and the use of end-extensions. Next we look at nonstandard finite permutations, introducing nonstandard symmetric and alternating groups. We show that the standard cut being strong is necessary and sufficient for coding of the cycle shape in the standard system to be equivalent to the cycle being contained within the external normal closure of the nonstandard symmetric group. Subsequently the normal subgroup structure of nonstandard symmetric and alternating groups is given as a result analogous to the result of Baer, Schreier and Ulam for infinite symmetric groups. The external structure of nonstandard cyclic groups of prime order is identified as that of infinite dimensional rational vector spaces and the normal subgroup structure of nonstandard projective special linear groups is given for models elementarily extending the standard model. Finally we discuss some applications of our measure to nonstandard finite groups.
[发布日期]  [发布机构] University:University of Birmingham;Department:School of Mathematics
[效力级别]  [学科分类] 
[关键词] Q Science;QA Mathematics [时效性] 
   浏览次数:3      统一登录查看全文      激活码登录查看全文