Search Results

The question I want to ask is close to but not exactly what stated in the title: Fix a language $L$, it is known that a statement $\sigma$ is universal in the language if whenever $M$ satisfies $\sig …

I am actually not reading the original paper "Diophantine problems over local fields, I (1965)" by Ax and Kochen but the revised version " The model theory of local fields (1975) " by Kochen which is …

This is a partial answer to the above question. It is too long for a comment. I write it hear hoping to hear idea from those senior than me, and in case it is useful. Here is some back ground, you mi …

I think that this question was down-rated too quickly. It appears to me that modulo the confusion which was pointed out by previous posts there are some valid point that need to be addressed. I just …

In this post I want to look at an issue I was in doubt when looking at the comment of F. G. Dorais in the post In model theory, does compactness easily imply completeness? F. G. Dorais remark was: …

According to Chang and Keisler's "Model Theory", Model Theory = Universal Algebra + Logic. Model theory generalized Universal Algebra in the sense that we allow relations while in Universal Algebra we …

Here is some more information for the first question. I think that to prove the meta theorems in mathematics, in particular, soundness, completeness, incompleteness, heuristic logic does not exhaust t …

Note: I have modified the question to make it clearer and more relevant. That makes some of references to the old version no longer hold. I hope the victims won't be furious over this. Motivation: …