The class of algebraically closed p-semilattices is finitely axiomatizable
Tóm tắt
We prove our title, and thereby establish the base for a positive solution of Albert and Burris’ problem on the finite axiomatizability of the model companion of the class of all pseudocomplemented semilattices.
Tài liệu tham khảo
Adler, J.: Model theoretic investigations of the class of pseudocomplemented semilattices. PhD thesis, University of Bern (1998)
Adler, J.: The model companion of the class of pseudocomplemented semilattices is finitely axiomatizable (2012, preprint)
Albert M.H., Burris S.N.: Finite axiomatizations for existentially closed posets and semilattices. Order 3, 169–178 (1986)
Chaida, I., Halaš, R., Kühr, J.: Semilattice structures. Research and Exp. in Math. Vol. 30, Heldermann, Lemgo (2007)
Frink O.: Pseudo-Complements in Semi-Lattices. Duke Math. J. 29, 504–515 (1962)
Hodges W.: A shorter model theory. Cambridge Univ. Press, Cambridge (1997)
Jones, G.-T.: Pseudocomplemented semilattices. PhD thesis, UCLA (1972)
Katriňák, T.: Die Kennzeichnung der distributiven pseudokomplementären Halbverbände. J. Reine Angew. Math. 241, 160–179 (1970) (German)
Pudlak P.: On congruence lattices of lattices. Algebra Universalis 20, 96–114 (1985)
Rupp, R.: On algebraically closed and existentially complete p-semilattices. PhD thesis, University of Bern (2006)
Schmid J.: Algebraically closed p-semilattices. Arch. Math. 45, 501–510 (1985)