Consequences ensuing from axioms.

Independence of purpose. The purpose/goal does not depend on the object (system) as it is determined not by the given object or its needs, but by the need of other object in something (is dictated by the external medium or other system). But the notion of “system” in relation to the given object depends on the purpose, i.e. on the adequacy of possibilities of the given object to execute the goal set. The goal is set from the outside and the object is tailored to comply with it, but not other way round. Only in this case the object presents a system. Note should be taken again of the singularity of the first consequence: the system's purpose/goal is determined by a need for something for some other object (external medium or other system). Common sense suggests that supposedly survivability is the need of the given organism (the given system). But it follows from the first consequence that the need to survive proceeds not from the given organism, but is set to it by another system external with respect to it, for example, the nature, and the organism tries to fulfill this objective.

Specialization of the system's functions. In response to certain (specific) external influence the system always produces certain (specific) result of action. Specialization means purposefulness. Any system is specialized (purposeful) and follows from the axiom. There are no systems in abstracto, there are systems that are concrete. Therefore, any system has its specific purpose/goal. Executive elements (executive SFU) of some systems may be homotypic (identical, non-differentiated from each other). If executive elements differ from each other (are multitype), the given system consists of differentiated elements.

System integrity. The system exerts itself as a unitary and integral object. It follows from the unity of purpose which is inherent only in the system as a whole, but not in its separate elements in particular. The purpose consolidates the system's elements in a comprehensive whole.

Limited discrecity of system. Nothing is indivisible and any system may be divided into parts. At the same time, any system consists of finite number of elements (parts): executive elements (subsystems, elements, SFU) and management elements (control block).

Hierarchy of system. The elements of a system relate to each other in varying ways and the place of each of them is the place on the hierarchic scale of the system. Hierarchy of systems is stipulated by hierarchy of purposes. Any system has a purpose. And to achieve this purpose it is necessary to achieve a number of smaller sub-goals for which the large system contains a number of subsystems of various degree of complexity, from minimum (SFU) up to maximum possible complexity. Hierarchy is the difference between the purposes of the system and the purposes of its elements (subsystems) which are the sub-goals in respect to it. At that, the systems of higher order set the goals before the systems of lower order. So, the purpose of the highest order is subdivided into a number of sub-goals (the purposes of lower order). The hierarchy of purposes determines the hierarchy of systems. To achieve each of the sub-goals specific element is required (it follows from the conservation law). Management/control in a hierarchic scale is performed in accordance with the law “the vassal of my vassal is not my vassal”. In other words, direct control is only possible at the level “system - own subsystem”, and the control by super system of the subsystem of its system is impossible. The tsar, should he wish to behead a criminal, would not do it himself, but would give a command to his subordinate executioner.

System function. The result of the system's performance is its function. To achieve the purpose the system should perform purposefully certain actions the result of which would be the system's function. The purpose is the argument for the system (imperative), while the result of action of the system is its function. The system's functions are determined by a set of executive elements, their relative positioning and control block. The notions of “system” and “function” are inseparable. Nonfunctional systems are non-existent. “Functional system” is a tautology, because all systems are functional. However, there may be systems which are non-operational at the moment (in a standby mode). Following certain external influence upon the system it will necessarily yield certain specific result of action (it will function). In the absence of the external influence the system produces no actions (does not function). When taking into account the purpose, the argument is not the external influence, but the purpose. One should distinguish internal functions of the system (sub-function) belonging to its elements (to subsystems, SFU) and the external functions belonging to the entire system as a whole. The system's external function of emergent property is the result of its own action produced by the system. Internal functions of the system are the results of action of its elements.

Effectiveness of systems. Correspondence of the result of action to the goal set characterizes the effectiveness of systems. Effectiveness of systems is directly linked with their function. The system's function in terms of effectiveness may be sufficient, it may by hyperfunction, decelerating and completely (absolutely) insufficient function. The system performs some actions and it leads to the production of the result of its action which should meet the purpose for which the given system is created. Effectiveness of systems is based on their specialization. “The boots should be sown by shoemaker”. Doing the opposite does not always result in real systems' actions that meet the target/preset results (partial effectiveness or its absence). The result of action of the system (its function) should completely correspond qualitatively and quantitatively to the preset purpose. It may mismatch, be incidental or even antagonistic (counter-purposeful); at that, real systems may produce all these kinds of results of action simultaneously. Only in ideal systems the result may completely meet the preset purpose (complete effectiveness). But systems with 100% performance factor are unknown to us. Integral result (integral function) is the sum of separate collateral/incidental and useful results of action. It is this sum that determines the appurtenance of the given object to the notion of “system” with regard to the given purpose. If the sum is positive, then with respect to the preset purpose the given object is a system of one or other efficiency. If the sum is equal to zero, the object is not a system with respect to the given purpose (neutral object). If the sum is negative, the given object is an anti-system (the system with minus sign preventing from the achievement of the goal/purpose). It applies both to systems and their elements. The higher the performance factor, the more effective the system is. Discrepancy of the result of action of the given system with the due value depends on unconformity of quantitative and qualitative resources of the system, for example, owing to breakage (destruction) or improper and/or insufficient development of its executive elements (SFU) and/or control. Therefore, any object is an element of a system only in the event that its actions (function) meet the achievement of the preset goal/purpose. Otherwise it is not an element of the given system. Effectiveness of systems is completely determined by limitation of actions of the systems.

Limitation of system's actions. Any system is characterized by qualitative and quantitative resources. The notion of resources includes the notion of functional reserve: what actions and how many of such actions the system may perform. Qualitative resources are determined by type of executive elements (SFU type), while quantitative resources by their quantity. And since real systems have certain and finite (limited) number of elements, it implies that real systems have limited qualitative and quantitative resources. “Qualitative resources” means “which actions” (or “what”) the given system is able to perform (to press, push, transfer, retain, supply, secrete, stand in somebody's light, etc.). “Quantitative resources” means “how many units of measure” (liters, mm Hg, habitation units, etc.) of such actions the given system is able to perform.

Discrecity (“quantal capacity”) of the system's functions. The system's actions are always discrete (quantized) as any of its SFU work under the “all-or-none” law. There exists no smooth change of the system's function, but there always exists phased (quantized) transition from one level of function to another, since executive elements actuate or deactivate regular SFU depending on the requirements of system. Transition of systems from one level of functions to another is always effected by way of a leap. We do not always observe this gradation/graduality because of the fact that the amplitude of the result of action of individual SFU can be very small, but still it is always there. The amplitude of these steps of transition from one level to another determines the maximum accuracy of the result of action of systems and is stipulated by the amplitude of the result of action of individual SFU (quantum of action). Probably, elementary particles are the most minimal SFU in our World and consequently indivisible into smaller parts subjected to laws of physics of our World.

Communicativeness of systems. Conjugate systems interact with each other. Such communication implicates the link/connection between the systems, i.e. their communicativeness. We discern open and closed systems. However, there are no completely isolated (closed) systems in our world which are not affected by some kind of external influence and which are nowise influencing any other systems. One may find at least two systems which are nowise interacting with each other (do not react) among themselves, but one can always find the third system (and probably the group of intermediate systems will be required) which will interact with (react to) the first two, i.e. be a link between them. If any system does not react at all to any influences exerted by any other systems and its own results of action are absolutely neutral with respect to other systems, and it is impossible to find the third system or a group of systems with which this system could interact (react to), it means that the given system does not exist in our World. Interaction between systems may be strong or weak, but it should be present, otherwise the systems do not exist for each other. Interaction is performed for the account of chains of actions: “... external influence > result of action...” By closing the end of such chain to its beginning we will get a closed (self-contained) system. The result of action after its “birth” does not depend on the system which has “gave birth” to it. Therefore, it may become external influence for the system itself. Then it will be a cyclically operating system, a generator with positive feedback. But the generator, too, requires for its performance the energy coming from the outside. Consequently, it is to some extent opened either. That is why the absolutely closed systems are non-existent. Each system has a certain number of internal and external links/connections (between the elements and between the systems, accordingly), through which the system may interact with other external systems. Closeness (openness) of a system is determined by the ratio of the number of internal and external links/connections. The larger the ratio, the greater the degree of closeness of a system is. Space objects of a “black holes” type are assumed to be referring to closed systems because even photons cannot break off from them. But they react with other space bodies through gravitation which means that they “are opened” through the gravitation channel through which they “evaporate” (disappear).

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