Only zero

In a recent paper, Bylinina and Nouwen claim that sentences involving the numeral zero are subject to obligatory exhaustification. This claim falls out as a result of two assumptions. First, that the pluralization operator x yields a full lattice structure, crucially including the bottom element, which has cardinality 0. This falls out from the definition of x. Second, that numerals give rise to an at least reading basically; the exactly reading is derived via exhaustification relative to excludable alternatives where the numeral varies. Here, Elliott, makes the novel observation that the numeral zero cannot associate with 'only.' Other numerals can, however, associate with only, obligatorily giving rise to an exactly reading. This is exactly what the author expect if 'only' and exh negate excludable alternatives.