Model theoryIn mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the statements of the theory hold). The aspects investigated include the number and size of models of a theory, the relationship of different models to each other, and their interaction with the formal language itself.
ChoiceA choice is the range of different things from which a being can choose. The arrival at a choice may incorporate motivators and models. For example, a traveler might choose a route for a journey based on the preference of arriving at a given destination at a specified time. The preferred (and therefore chosen) route can then account for information such as the length of each of the possible routes, the amount of fuel in the vehicle, traffic conditions, etc.
Family valuesFamily values, sometimes referred to as familial values, are traditional or cultural values that pertain to the family's structure, function, roles, beliefs, attitudes, and ideals. In the social sciences and U.S. political discourse, the conventional term "traditional family" describes the nuclear family—a child-rearing environment composed of a breadwinning father, a homemaking mother, and their nominally biological children. A family deviating from this model is considered a nontraditional family.
Label (sociology)A label is an abstract concept in sociology used to group people together based on perceived or held identity. Labels are a mode of identifying social groups. Labels can create a sense of community within groups, but they can also cause harm when used to separate individuals and groups from mainstream society. Individuals may choose a label, or they may be assigned one by others. The act of labeling may affect an individual's behavior and their reactions to the social world.
Axiom of dependent choiceIn mathematics, the axiom of dependent choice, denoted by , is a weak form of the axiom of choice () that is still sufficient to develop most of real analysis. It was introduced by Paul Bernays in a 1942 article that explores which set-theoretic axioms are needed to develop analysis. A homogeneous relation on is called a total relation if for every there exists some such that is true. The axiom of dependent choice can be stated as follows: For every nonempty set and every total relation on there exists a sequence in such that for all In fact, x0 may be taken to be any desired element of X.
