Mattress for a bed system having a lying surface, - with a foam core having a core upper side facing the lying surface and a core underside facing away from the lying surface, - with a lifting device for adjusting the height of at least one lying surface zone of the lying surface of the bed system, wherein the respective lying surface zone extends in a longitudinal direction of the lying surface over only a part of the entire lying surface length of the lying surface and in a transverse direction of the lying surface running perpendicular to the longitudinal direction of the lying surface over the entire lying surface width of the lying surface, - with a mattress cover, which envelops the foam core and the lifting device and which has the lying surface, - wherein the lifting device has at least one lifting unit, which is specifically assigned to a lying surface zone and which has at least one lifting element pair, which has exactly two hydraulic or pneumatic lifting elements and exactly one cross member, which extends parallel to the transverse direction of the lying surface and connects the two lifting elements to one another, - wherein at least one such lifting unit has a plurality of lifting element pairs, which are arranged next to one another in the longitudinal direction of the lying surface, - wherein the lifting device has a control device, which has at least one pumping device for conveying a fluid and a valve device, - wherein the lifting device has a plurality of fluid lines for fluidic coupling of the lifting elements with the control device, - wherein the lifting device has an actuating device for manually actuating the lifting device, - wherein an actuation to raise the respective lying surface zone is effected by the lifting elements of the lifting unit assigned to this lying surface zone being inflated, such that the lifting elements of the respective lifting element pair raise the associated cross member, - wherein an actuation to lower the respective lying surface zone is effected by the lifting elements of the lifting unit assigned to this lying surface zone being deflated, such that the lifting elements of the respective lifting element pair lower the associated cross member, - wherein the foam core has a recess on its core underside for the respective lifting element pair, into which the respective lifting element pair is inserted such that it does not protrude beyond the core underside. - with a foam core having a core upper side facing the lying surface and a core underside facing away from the lying surface, - with a lifting device for adjusting the height of at least one lying surface zone of the lying surface of the bed system, wherein the respective lying surface zone extends in a longitudinal direction of the lying surface over only a part of the entire lying surface length of the lying surface and in a transverse direction of the lying surface running perpendicular to the longitudinal direction of the lying surface over the entire lying surface width of the lying surface, - with a mattress cover, which envelops the foam core and the lifting device and which has the lying surface, - wherein the lifting device has at least one lifting unit, which is specifically assigned to a lying surface zone and which has at least one lifting element pair, which has exactly two hydraulic or pneumatic lifting elements and exactly one cross member, which extends parallel to the transverse direction of the lying surface and connects the two lifting elements to one another, - wherein at least one such lifting unit has a plurality of lifting element pairs, which are arranged next to one another in the longitudinal direction of the lying surface, - wherein the lifting device has a control device, which has at least one pumping device for conveying a fluid and a valve device, - wherein the lifting device has a plurality of fluid lines for fluidic coupling of the lifting elements with the control device, - wherein the lifting device has an actuating device for manually actuating the lifting device, - wherein an actuation to raise the respective lying surface zone is effected by the lifting elements of the lifting unit assigned to this lying surface zone being inflated, such that the lifting elements of the respective lifting element pair raise the associated cross member, - wherein an actuation to lower the respective lying surface zone is effected by the lifting elements of the lifting unit assigned to this lying surface zone being deflated, such that the lifting elements of the respective lifting element pair lower the associated cross member, - wherein the foam core has a recess on its core underside for the respective lifting element pair, into which the respective lifting element pair is inserted such that it does not protrude beyond the core underside.