Active address keys (AAK) are translated into respective addressabilities in physical main memory. Each addressability comprises one or more physical blocks which may be scattered in the main memory. Each address key represents the assigned addressability in main memory for a logical address space. Plural key register sections may be loaded with the same or different address keys. For each storage access request, received from a processor or I/O channel, AAK select circuits outgate to the translator the key in the key register section corresponding to the type of the current storage access request to determine the addressability available to the access request. Each address key identifies a particular stack of one or more segmentation registers. Each segmentation register can be assigned the address of any segment (i.e. a block of contiguous physical addresses located anywhere in the main memory). Each segmentation register also has validity and read-only flag bits for its assigned block. Each stack can translate a contiguous set of logical addresses into physical addresses. For each storage access request for a logical address, and not apparent to the usury program, a stack is addressed by the AAK to translate the logical address to a real address within the assigned addressability. Then a register in the stack is selected by high-order bits in the logical address. The addressed register outputs an assigned block address. Low order bits in the logical address select a byte address in the assigned block. The main memory can have any physical size, which is coordinated with the number of stacks, and to the number of segmentation registers in each stack.