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The First Order is a fictional military movement and rump state [1] in the Star Wars franchise, introduced in the 2015 film The Force Awakens.It is formed following the fall of the Galactic Empire after the events of Return of the Jedi (1983).
First-order logic, a formal logical system used in mathematics, philosophy, linguistics, and computer science; First-order predicate, a predicate that takes only individual(s) constants or variables as argument(s) First-order predicate calculus; First-order theorem provers; First-order theory; Monadic first-order logic
First-order logic also satisfies several metalogical theorems that make it amenable to analysis in proof theory, such as the Löwenheim–Skolem theorem and the compactness theorem. First-order logic is the standard for the formalization of mathematics into axioms, and is studied in the foundations of mathematics.
This is not a first-order axiomatization as one of Hilbert's axioms is a second order completeness axiom. Tarski's axioms are a first-order axiomatization of Euclidean geometry. Tarski showed this axiom system is complete and decidable by relating it to the complete and decidable theory of real closed fields.
The corresponding first-order theory is the set of sentences that are actually true of the real numbers. There are several different such theories, with different expressive power, depending on the primitive operations that are allowed to be used in the expression.
In mathematical logic, a first-order predicate is a predicate that takes only individual(s) constants or variables as argument(s). [1] Compare second-order predicate and higher-order predicate . This is not to be confused with a one-place predicate or monad, which is a predicate that takes only one argument.
The Order II, which is also known as the Bruder Schweigen Strike Force II, was an attempt to perpetuate the activities of the first Order by David and Deborah Dorr, both of whom were previously members of the Aryan Nations, but their activities were confined to the state of Idaho. [39]
A first-order reduction is a reduction where each component is restricted to be in the class FO of problems calculable in first-order logic. Since we have FO ⊊ L {\displaystyle {\mbox{FO}}\subsetneq {\mbox{L}}} , the first-order reductions are stronger reductions than the logspace reductions .