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2. First-order logic - Wikipedia

   en.wikipedia.org/wiki/First-order_logic

   First-order logic —also called predicate logic, predicate calculus, quantificational logic —is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables.

3. Order (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Order_(mathematics)

   Order theory, study of various binary relations known as orders. Order topology, a topology of total order for totally ordered sets. Ordinal numbers, numbers assigned to sets based on their set-theoretic order. Partial order, often called just "order" in order theory texts, a transitive antisymmetric relation.

4. Order (group theory) - Wikipedia

   en.wikipedia.org/wiki/Order_(group_theory)

   For example, in the symmetric group shown above, where ord(S 3) = 6, the possible orders of the elements are 1, 2, 3 or 6. The following partial converse is true for finite groups : if d divides the order of a group G and d is a prime number , then there exists an element of order d in G (this is sometimes called Cauchy's theorem ).

5. List of first-order theories - Wikipedia

   en.wikipedia.org/wiki/List_of_first-order_theories

   Use ordinary first-order logic, but add a new unary predicate "Set", where "Set(t)" means informally "t is a set". Use ordinary first-order logic, and instead of adding a new predicate to the language, treat "Set(t)" as an abbreviation for "∃y t∈y" Some first-order set theories include: Weak theories lacking powersets:

6. Word order - Wikipedia

   en.wikipedia.org/wiki/Word_order

   t. e. In linguistics, word order (also known as linear order) is the order of the syntactic constituents of a language. Word order typology studies it from a cross-linguistic perspective, and examines how languages employ different orders. Correlations between orders found in different syntactic sub-domains are also of interest.

7. Transitive relation - Wikipedia

   en.wikipedia.org/wiki/Transitive_relation

   Symbolic statement. In mathematics, a binary relation R on a set X is transitive if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates a to c. Every partial order and every equivalence relation is transitive. For example, less than and equality among real numbers are both transitive: If a < b and b < c ...