New technique of constructive designing of counterexamples to the interpolation property and Beth property was developed. It was proved that the intuitionistic logic of finite domains has neither interpolation nor the Beth property by using this technique. Also was found the first example of the predicate intermediate logic without Beth property. It is established that for any propositional superintuitionistic logic L there exists a continuum of predicate superintuitionistic logic with equality, whose propositional fragment is L and which do not possess the Beth property and interpolation property. Also there exists a continuum of predicate superintuitionistic logic without equality that have not Beth property and interpolation property. It was shown that the fragment of predicate intuitionistic logic in the language without the disjunction and existential quantifier coincides with a similar fragment of logic of constant domains. It was proved that this fragment has interpolation property and Beth property. Although the intuitionistic logic of finite domains has neither interpolation nor the Beth property the fragment of this logic in the language without disjunction and existential quantifier enjoys both properties.
Biography
Graduated from Faculty of Mathematics and Mechanics Novosibirsk State University (NSU) in 1993 (department of algebra and mathematical logic). Master degree was received in 1995. Ph.D. thesis was defended in 1998. A list of my works contains 23 titles.
Main publications:
Schreiner P. A. Continua of superintuitionistic predicate logics without Beth's property.
Schreiner P.A. Fragment of Logic of Finite Constant Domains Without Disjunction and Existential Quantifier, Abstract of contributed papers, LC2000 and ELSS2000. Paris: La Sorbonne, 2000, 247.
P. A. Schreiner, “Automatic recognition of interpolation in modal calculi”, Algebra Logika, 46:1 (2007), 103–119; Algebra and Logic, 46:1 (2007), 62–70
L. L. Maksimova, P. A. Schreiner, “Algorithms of the recognition of the tabularity and pretabularity in the extensions of the intuitionistic calculus”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 6:3 (2006), 49–58
P. A. Schreiner, “On a fragment of intuitionistic logic that is complete with respect to the Kripke frames with finite domains”, Sibirsk. Mat. Zh., 41:2 (2000), 470–479; Siberian Math. J., 41:2 (2000), 389–396
1998
4.
P. A. Schreiner, “Intermediate predicate logic without the Beth property”, Algebra Logika, 37:1 (1998), 107–117
1996
5.
P. A. Schreiner, “Absence of interpolation in some predicate superintuitionistic
logics”, Algebra Logika, 35:1 (1996), 105–117