Abstract: | We deal with the decidability problem for first-order theories of a complete linear group GL(n,ℤ) of all integral matrices
of order n ≥ 3. and of a respective complete linear monoid ML(n,ℤ). It is proved that theories ∀? ∧ GL(3,ℤ). ∃∀∧ GL(3,ℤ).
∀? ∧ ML(3,ℤ), and ∃? ∧ ML(3,ℤ) are critical. and that ∃∀ ∧ νGL(n,ℤ) and ∃∀ ∧ML(n,ℤ) are decidable for any n ≥ 3.
Translated fromAlgebra i Logika, Vol. 39, No. 4, pp. 480–504, July–August, 2000. |