Model-theoretic properties characterizing Peano arithmetic
Model-theoretic properties characterizing Peano arithmetic
复制标题
表征皮亚诺算术的模型理论特性
DOI：
10.2307/2275063
复制
发表时间：
1991
影响因子：
0.6
通讯作者：
R. Kaye
中科院分区：
文献类型：
--
作者：
R. Kaye
摘要 设 = {0,1, +,·,<} 是通常的一阶算术语言。我们证明皮亚诺算术是包含 IΔ0 + exp 的最小一阶理论，使得它的每个完整扩展 T 都有一个可数模型 K 满足 (i) K 没有适当的基本子结构，并且 (ii) 每当 L ≻ K 是一个可数基本扩展时，就有 。还讨论并展示了类似于 (i) 和 (ii) 的其他模型理论条件，以表征皮亚诺算术。
Abstract Let = {0,1, +,·,<} be the usual first-order language of arithmetic. We show that Peano arithmetic is the least first-order -theory containing IΔ0 + exp such that every complete extension T of it has a countable model K satisfying (i) K has no proper elementary substructures, and (ii) whenever L ≻ K is a countable elementary extension there is and such that . Other model-theoretic conditions similar to (i) and (ii) are also discussed and shown to characterize Peano arithmetic.