EVERY 2 ELEMENTARILY EQUIVALENT MODELS HAVE ISOMORPHIC ULTRAPOWERS
EVERY 2 ELEMENTARILY EQUIVALENT MODELS HAVE ISOMORPHIC ULTRAPOWERS
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DOI：
10.1007/bf02771574
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发表时间：
1971-01-01
影响因子：
1
通讯作者：
SHELAH, S
中科院分区：
文献类型：
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作者：
SHELAH, S
这个定理推广了Keisler [6]（它用GCH证明了一个更强的结果），证明推广了Kunen [12]的证明。定理的第（1）部分肯定了一个著名的猜想，但不清楚是谁提出的，它作为公开问题5出现在Chang和Keisler [1]中。几个人从几个方面对这个问题进行了探讨。Keisler [6]证明：如果2+= 2 z，则存在2上的超滤子D，使得：如果M-N，I1 M] 1 < 2 + 11N [I<;~+，且语言的基数<2，则MaID”~ NX/D。Keisler [8]将其分解为以下几个阶段：若2+= 2~，则存在2上的2+-好超滤子;若D是I上的2+-好超滤子，M是基数_-< 2的语言模型，则MIlD是2+-饱和的，且任意两个基数为p的初等等价p-饱和模型同构。(See Keisler [8]，Keisler [7] and莫利and Vaught [15]）.另一种方法是Kochen [11]（或Keisler [10] § 5）。何根-
This theorem generalizes Keisler [6](which proved a stronger result using GCH) and the proof generalizes the proof of Kunen [12]. Part (1) of the theorem affirms a well-known conjecture; it is not clear who proposed it. It occurs as open problem 5 in Chang and Keisler [1]. The problem was attacked by several people in several ways. Keisler [6] proves: if 2+= 2 z, then there is an ultrafilter D over 2 such that: if M----N, I1M] l< 2+'11N [I<;~+, and the language is of cardinality< _ 2 then MaID"~ NX/D. By Keisler [8] this can be broken into the following stages: if 2+= 2~, there is a 2+-good ultrafilter over 2; if D is a 2+-good ultrafilter over I and M a model with language of cardinality _-< 2, then MIlD is 2+-saturated, and any two elementarily equivalent p-saturated models of cardinality p are isomorphic.(See Keisler [8], Keisler [7] and Morley and Vaught [15]). Another approach was that of Kochen [11](or Keisler [10] § 5). He gen-