• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Journal of logic and computation >Infinity, in short
【24h】

Infinity, in short

机译：简而言之，无限

获取原文
获取原文并翻译 | 示例
       
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

It is shown that within the language of Set Theory, if membership is assumed to be non-well-founded a la Aczel, then one can state the existence of infinite sets by means of an (EEAA) prenex sentence. Somewhat surprisingly, this statement of infinity is essentially the one which was proposed in 1988 for well-founded sets, and it is satisfied exclusively by well-founded sets. Stating infinity inside the BSR (Bernays-Schonfinkel-Ramsey) class of the (E *A*)-sentences becomes more challenging if no commitment is taken as whether membership is well-founded or not: for this case, we produce an (EEAA)-sentence, thus lowering the complexity of the quantificational prefix with respect to earlier prenex formulations of infinity. We also show that no prenex specification of infinity can have a prefix simpler than (EEAA). The problem of determining whether a BSR-sentence involving an uninterpreted predicate symbol and = can be satisfied over a large domain is then reduced to the satisfiability problem for the set theoretic class BSR subject to the ill-foundedness assumption. Envisaged enhancements of this reduction, cleverly exploiting the expressive power of the set theoretic BSR-class, add to the motivation for tackling the satisfaction problem for this class, which appears to be anything but unchallenging.
机译：结果表明，在集合论的语言中，如果假定隶属关系不充分，则可以通过（EEAA）前言语句来说明无限集的存在。出乎意料的是，这种无穷大的陈述本质上是1988年针对有良好基础的集合所提出的，并且仅由有良好基础的集合满足。如果不考虑成员资格是否成立，则在（E * A *）句子的BSR（Bernays-Schonfinkel-Ramsey）类内部声明无限会变得更具挑战性：在这种情况下，我们产生（EEAA） ）句子，因此相对于较早的无穷大prenex公式而言，降低了量化前缀的复杂性。我们还表明，无穷大的prenex规范不能具有比（EEAA）更简单的前缀。然后将确定是否可以在大范围内满足涉及未解释的谓词符号和=的BSR句子的问题，归结为适用于理论基础不佳的假设的集合理论类BSR的可满足性问题。设想的这种减少的增强，可以巧妙地利用集合理论BSR类的表达能力，从而增加了解决此类类满意度问题的动机，这似乎没有什么挑战性。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号