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A symbol used to represent a Boolean statement in logic that can take the value either true or false. All statement letters are statements forms (Mendelson 1997, p. 13).

A formal argument in logic in which it is stated that 1. P=>Q and R=>S (where => means "implies"), and 2. Either not-Q or not-S is true, from which two statements it follows ...

In December 1920, M. Schönfinkel presented in a report to the Mathematical Society in Göttingen a new type of formal logic based on the concept of a generalized function ...

Propositional calculus, first-order logic, and other theories in mathematical logic are defined by their axioms (or axiom schemata, plural: axiom schemata) and inference ...

A formula of first-order logic is in prenex normal form if it is of the form Q_1x_1...Q_nx_nM, (1) where each Q_i is a quantifier forall ("for all") or exists ("exists") and ...

One of the operations exists exists (called the existential quantifier) or for all forall (called the universal quantifier, or sometimes, the general quantifier). However, ...

The Kreisel conjecture is a conjecture in proof theory that postulates that, if phi(x) is a formula in the language of arithmetic for which there exists a nonnegative integer ...

Nonstandard analysis is a branch of mathematical logic which introduces hyperreal numbers to allow for the existence of "genuine infinitesimals," which are numbers that are ...

The Paris-Harrington theorem is a strengthening of the finite Ramsey's theorem by requiring that the homogeneous set be large enough so that cardH>=minH. Clearly, the ...

A statement which is rigorously known to be correct. A statement which is not true is called false, although certain statements can be proved to be rigorously undecidable ...