TY - JOUR

T1 - On the for all there exists-Theories of Free Projective Planes

AU - Kogabaev, N. T.

PY - 2020/1

Y1 - 2020/1

N2 - Studying the elementary properties of free projective planes of finite rank, we prove that for m > n, an arbitrary for all there exists for all-formula phi(& x233;) and a tuple u of elements of the free projective plane Fn if phi(u) holds on the plane Fm then phi(u) holds on the plane Fn too. This implies the coincidence of the for all there exists-theories of free projective planes of different finite ranks.

AB - Studying the elementary properties of free projective planes of finite rank, we prove that for m > n, an arbitrary for all there exists for all-formula phi(& x233;) and a tuple u of elements of the free projective plane Fn if phi(u) holds on the plane Fm then phi(u) holds on the plane Fn too. This implies the coincidence of the for all there exists-theories of free projective planes of different finite ranks.

KW - elementary theory

KW - for all there exists-theory

KW - projective plane

KW - free projective plane

KW - configuration

KW - incidence

KW - ELEMENTARY THEORY

KW - HOMOMORPHISMS

U2 - 10.1134/S0037446620010085

DO - 10.1134/S0037446620010085

M3 - Article

VL - 61

SP - 95

EP - 108

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 1

ER -