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The Physiocrats, a group of 18th century Enlightenment French philosophers, thought there was a "natural order" that allowed human beings to live together. According to them it is an ideal order given to them by God, which allowed human beings to live together in an ideal society. The natural laws are the expression of the will of God.
Order theory is a branch of mathematics that investigates ... The first order often discussed in primary school is the standard order on the natural numbers e.g. "2 ...
Natural law [1] (Latin: ius naturale, lex naturalis) is a system of law based on a close observation of natural order and human nature, from which values, thought by natural law's proponents to be intrinsic to human nature, can be deduced and applied independently of positive law (the express enacted laws of a state or society). [2]
Spontaneous order, also named self-organization in the hard sciences, is the spontaneous emergence of order out of seeming chaos. The term "self-organization" is more often used for physical changes and biological processes, while "spontaneous order" is typically used to describe the emergence of various kinds of social orders in human social networks from the behavior of a combination of self ...
It is an open problem whether this theory is decidable, but if Schanuel's conjecture holds then the decidability of this theory would follow. [2] [3] In contrast, the extension of the theory of real closed fields with the sine function is undecidable since this allows encoding of the undecidable theory of integers (see Richardson's theorem).
The theory of the natural numbers with a successor function is complete and decidable, and is κ-categorical for uncountable κ but not for countable κ. Presburger arithmetic is the theory of the natural numbers under addition, with signature consisting of a constant 0, a unary function S, and a binary function +. It is complete and decidable.
Order theory is a branch of mathematics that studies various kinds of objects (often binary relations) that capture the intuitive notion of ordering, providing a framework for saying when one thing is "less than" or "precedes" another. An alphabetical list of many notions of order theory can be found in the order theory glossary.
Presburger arithmetic is the first-order theory of the natural numbers with addition, named in honor of Mojżesz Presburger, who introduced it in 1929.The signature of Presburger arithmetic contains only the addition operation and equality, omitting the multiplication operation entirely.