Abstract
Abstract—
We prove $$\Sigma _{1}^{0}$$-hardness of a number of theories of a binary predicate with three individual variables (in languages without constants or equality). We also show that, in languages with equality and the operators of composition and of transitive closure, theories of a binary predicate are $$\Pi _{1}^{1}$$-hard with only two individual variables.
Reference24 articles.
1. E. Börger, E. Grädel, and Yu. Gurevich, The Classical Decision Problem (Springer, Berlin, 1997).
2. Yu. L. Ershov, I. A. Lavrov, A. D. Taimanov, and M. A. Taitslin, “Elementary theories,” Russ. Math. Surv. 20 (4), 35–105 (1965).
3. A. Nies, “Undecidable fragments of elementary theories,” Algebra Univers. 35, 8–33 (1996).
4. G. S. Boolos, J. P. Burgess, and R. C. Jeffrey, Computability and Logic, 5th ed. (Cambridge Univ. Press, Cambridge, 2007).
5. J. Surányi, “Zur Reduktion des Entscheidungsproblems des logischen Funktioskalküls,” Math. Fiz. Lapok 50, 51–74 (1943).
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