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Decidability of first-order theories of the real numbers
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<h2 id="see-also">See also</h2> <ul><li><a href="/facts/Construction_of_the_real_numbers/rxoyDRav">Construction of the real numbers</a></li> <li><a href="/facts/Tarski%27s_axiomatization_of_the_reals/b2bIKIR2">Tarski's axiomatization of the reals</a></li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>A. Burdman Fefferman and S. Fefferman, Alfred Tarski: Life and Logic (Cambridge: Cambridge University Press, 2008). <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Macintyre, A.J.; Wilkie, A.J. (1995), "On the decidability of the real exponential field", in Odifreddi, P.G. (ed.), Kreisel 70th Birthday Volume, CLSI <a href="/wiki/Archibald_James_Macintyre" target="_blank">/wiki/Archibald_James_Macintyre</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Kuhlmann, S. (2001) [1994], "Model theory of the real exponential function", Encyclopedia of Mathematics, EMS Press <a href="https://www.encyclopediaofmath.org/index.php?title=Model_theory_of_the_real_exponential_function" target="_blank">https://www.encyclopediaofmath.org/index.php?title=Model_theory_of_the_real_exponential_function</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Ratschan, Stefan (2006). "Efficient Solving of Quantified Inequality Constraints over the Real Numbers". ACM Transactions on Computational Logic. 7 (4): 723–748. arXiv:cs/0211016. doi:10.1145/1183278.1183282. S2CID 16781766. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>Akbarpour, Behzad; Paulson, Lawrence Charles (2010). "MetiTarski: An Automatic Theorem Prover for Real-Valued Special Functions". Journal of Automated Reasoning. 44 (3): 175–205. doi:10.1007/s10817-009-9149-2. S2CID 16215962. <a href="/wiki/Lawrence_Paulson" target="_blank">/wiki/Lawrence_Paulson</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> </ol>