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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, so that rather than ...

3. List of first-order theories - Wikipedia

   en.wikipedia.org/wiki/List_of_first-order_theories

   List or describe a set of sentences in the language L σ, called the axioms of the theory. Give a set of σ-structures, and define a theory to be the set of sentences in L σ holding in all these models. For example, the "theory of finite fields" consists of all sentences in the language of fields that are true in all finite fields. An L σ ...

4. Theory (mathematical logic) - Wikipedia

   en.wikipedia.org/wiki/Theory_(mathematical_logic)

   Theory (mathematical logic) In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. In most scenarios a deductive system is first understood from context, after which an element of a deductively closed theory is then called a theorem of the theory. In many deductive systems there is usually a ...

5. Elementary arithmetic - Wikipedia

   en.wikipedia.org/wiki/Elementary_arithmetic

   Elementary arithmetic. The symbols for elementary-level math operations. From top-left going clockwise: addition, division, multiplication, and subtraction. Elementary arithmetic is a branch of mathematics involving addition, subtraction, multiplication, and division. Due to its low level of abstraction, broad range of application, and position ...

6. Propositional calculus - Wikipedia

   en.wikipedia.org/wiki/Propositional_calculus

   Propositional calculus. The propositional calculus [a] is a branch of logic. [1] It is also called propositional logic, [2] statement logic, [1] sentential calculus, [3] sentential logic, [1] or sometimes zeroth-order logic. [4] [5] It deals with propositions [1] (which can be true or false) [6] and relations between propositions, [7] including ...

7. Decidability of first-order theories of the real numbers

   en.wikipedia.org/wiki/Decidability_of_first...

   In mathematical logic, a first-order language of the real numbers is the set of all well-formed sentences of first-order logic that involve universal and existential quantifiers and logical combinations of equalities and inequalities of expressions over real variables. The corresponding first-order theory is the set of sentences that are ...