I am wondering what other decidable theorem or results that is not weaker or stronger than Tarski's theorem.
Could any one give reference or a simple introduction about such result known in their domain?
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asked Nov 25, 2014 at 11:21
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3$\begingroup$ Which Tarski's theorem do you have in mind? I think he had few... $\endgroup$– WojowuCommented Nov 25, 2014 at 11:26
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$\begingroup$ @Wojowu, thank you for your comments, which one of his theorems is about decidability? $\endgroup$– XL _At_Here_ThereCommented Nov 25, 2014 at 11:40
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2$\begingroup$ One theorem of his shows that theory of real ordered fields is decidable, another says so about his axiomatization of Euclidean geometry. Tarski's undefinability theorem can also be thought as concerning decidability (there is no predicate which "decides" truth of statements). $\endgroup$– WojowuCommented Nov 25, 2014 at 11:46
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4$\begingroup$ Tarski has many results on decidability. The whole Tarski-Mostowski-Robinson monograph is devoted to undecidability of theories. $\endgroup$– Emil JeřábekCommented Nov 25, 2014 at 12:12
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$\begingroup$ @EmilJeřábek, you are so severe on any questions, like an excellent judge in supremcourt. But let us list the decidable result near or above any theorems relating Tarski. $\endgroup$– XL _At_Here_ThereCommented Nov 26, 2014 at 1:29
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1 Answer
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Ax and Kochen proved decidability for the ring of $p$-adic numbers, and many rings like it. That certainly doesn't follow from Tarski, and I would say it is more difficult.
answered Nov 25, 2014 at 14:40
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$\begingroup$ Yes, excellent, David, although I had read their paper several weeks ago. I hope we can have a complete or almost complete list of such answers so as to have an overview of the decidable problem $\endgroup$ Commented Nov 26, 2014 at 0:19