论局部句的可判定性
On Decidability Properties of Local Sentences
摘要：
当地（一阶）的句子，介绍了Ressayre，享有非常好的可判定性的性质，以下从一些拉伸定理说明一些显着的联系之间的有限和无限的模型理论，这些句子。我们在这里证明了几个额外的本地句子的结果。第一个是一个新的可判定性结果的情况下，当地的句子，其功能符号是最多一元：一个可以决定，为每一个经常基数k是否一个当地的句子phi有一个模型的顺序类型k。其次，我们证明了这个结果不能推广到一般情况。在不可达基数的相容性假设下，证明了序型为ω_2的局部句子集不是由公理系统ZFC + GCH决定的，这里GCH是广义连续统假设
英文摘要：
Local (first order) sentences, introduced by Ressayre, enjoy very nice decidability properties, following from some stretching theorems stating some remarkable links between the finite and the infinite model theory of these sentences. We prove here several additional results on local sentences. The first one is a new decidability result in the case of local sentences whose function symbols are at most unary: one can decide, for every regular cardinal k whether a local sentence phi has a model of order type k. Secondly we show that this result can not be extended to the general case. Assuming the consistency of an inaccessible cardinal we prove that the set of local sentences having a model of order type omega_2 is not determined by the axiomatic system ZFC + GCH, where GCH is the generalized continuum hypothesis
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