The determinants of excessive indebtedness of the rural poor
ConclusionThe foregoing analysis helps to explain how the poverty cycle deepens and becomes increasingly intolerable for the rural poor.
Correlates of rural black poverty
ConclusionThe misery of America’s rural black farmers and farm workers continue as a reproach to the nation; black farmers and farm workers, numbering about 328,000 in 1970, have not adequately shared in the enormous productivity of American agriculture and in the rising prosperity of the nation.Despite modest steps to improve their level of living, they remain, by and large, at subpoverty-income levels, lacking adequate health care, ill-housed, malnourished, and poorly educated.6 The annual migration rate of rural black youth is insignificantly lower today than during the great migration flows following the world wars; this is a testimony to the barrenness of the alternative lifestyle under which they might live.
Decidability of some intuitionistic predicate theories
Suppose T is a first order intuitionistic theory (more precisely, a theory of Heyting's predicate calculus, e.g., abelian groups, one unary function, dense linear order, etc.) presented to us by a set of axioms (denoted also by) T. Question. Is T decidable? One knows that if the classical counterpart of T (i.e., take the same axioms but with the classical predicate calculus as the underlying logic) is not decidable, then T cannot be decidable. The problem remains for theories whose classical counterpart is decidable. In [8], sufficient conditions for undecidability were given, and several intuitionistic theories such as abelian groups and unary functions (both with decidable equality) were shown to be undecidable. In this note we show decidability results (see Theorems 1 and 2 below), and compare these results with the undecidability results previously obtained. The method we use is the reduction-method, described fully in [12] and widely applied in [3], which is applied here roughly as follows: Let T be a given theory of Heyting's predicate calculus. We know that Heyting's predicate calculus is complete for the Kripke-model type of semantics. We choose a class M of Kripke models for which T is complete, i.e., all axioms of T are valid in any model of the class and whenever φ is not a theorem of T, φ is false in some model of M.