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searching for Metatheorem 8 found (24 total)

Hypothetical syllogism (1,326 words) [view diff] no match in snippet view article find links to article

In classical logic, a hypothetical syllogism is a valid argument form, a deductive syllogism with a conditional statement for one or both of its premises

Hilbert system (3,381 words) [view diff] exact match in snippet view article find links to article

axiomatisation using an extra rule of generalisation (see the section on Metatheorems), in which case the rules Q6 and Q7 are redundant.[dubious – discuss]

Double negation (1,172 words) [view diff] exact match in snippet view article find links to article

φ0. We also use repeatedly the method of the hypothetical syllogism metatheorem as a shorthand for several proof steps. (1) φ 0 {\displaystyle \varphi

Contraposition (6,075 words) [view diff] exact match in snippet view article find links to article

Hypothetical syllogism. We also use the method of the hypothetical syllogism metatheorem as a shorthand for several proof steps. The proof is as follows: q →

Implicational propositional calculus (3,081 words) [view diff] exact match in snippet view article find links to article

proof of A. The axioms listed above primarily work through the deduction metatheorem to arrive at completeness. Here is another axiom system that aims directly

Sanskrit (32,143 words) [view diff] exact match in snippet view article find links to article

stratifying out use and mention, language and metalanguage, and theorem and metatheorem predate key discoveries in western philosophy by millennia." "The Sanskrit

Heyting arithmetic (6,233 words) [view diff] exact match in snippet view article find links to article

This impacts the logic: With 1 := S 0 {\displaystyle 1:=S0} , it is a metatheorem that ⊥ {\displaystyle \bot } can be defined as 0 = 1 {\displaystyle 0=1}

Constructive set theory (34,880 words) [view diff] exact match in snippet view article find links to article

range being a set does not suffice to be granted a function set. It is a metatheorem for theories containing B C S T {\displaystyle {\mathsf {BCST}}} that