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A sentential variable, also called a propositional variable, that can be substituted for in arbitrary sentential formulas (Carnap 1958, p. 24).

An expression built up from statements letters by appropriate application of connectives (Mendelson 1997, p. 13).

A syllogism, also known as a rule of inference, is a formal logical scheme used to draw a conclusion from a set of premises. An example of a syllogism is modus ponens.

A theory is a set of sentences which is closed under logical implication. That is, given any subset of sentences {s_1,s_2,...} in the theory, if sentence r is a logical ...

If the property of being an object is expressed by a basic predicate of the system, then such a predicate (if it exists) is called a universal predicate, or universal ...

A property of individuals which is shared by every individual.

The quantifier "for all" ( forall ), sometimes also known as the "general quantifier."

A universal sentence is a sentence (i.e., formula of the predicate calculus without free variables) whose variables are universally quantified.

For any sets A and B, their cardinal numbers satisfy |A|<=|B| iff there is a one-to-one function f from A into B (Rubin 1967, p. 266; Suppes 1972, pp. 94 and 116). It is easy ...

A Colbert number is any prime number with more than 1000000 decimal digits whose discovery contributes to the long-sought after proof that k=78557 is the smallest Sierpiński ...