axiom of comprehension
An axiom schema of set theory which states: if P(x) is a property then
x : P
is a set. I.e. all the things with some property form a set.
Acceptance of this axiom leads to Russell’s Paradox which is why Zermelo set theory replaces it with a restricted form.
- Axiom schema
axiom schema logic A formula in the language of an axiomatic system, containing one or more. These metasyntactic variables (or “schematic variables”) that stand for terms or subformulae. An example is the Axiom of Comprehension. (2009-02-10)
pertaining to or of the nature of an axiom; self-evident; obvious. aphoristic. Contemporary Examples When you pay them more, it is axiomatic that they will spend more. Obama Should Take on the Private Sector’s Wage Delusion Daniel Gross July 23, 2013 After Vietnam, it was axiomatic that the press would approach those in power with […]
- Axiomatic set theory
axiomatic set theory theory One of several approaches to set theory, consisting of a formal language for talking about sets and a collection of axioms describing how they behave. There are many different axiomatisations for set theory. Each takes a slightly different approach to the problem of finding a theory that captures as much as […]
- Axiomatic semantics
axiomatic semantics theory A set of assertions about properties of a system and how they are effected by program execution. The axiomatic semantics of a program could include pre- and post-conditions for operations. In particular if you view the program as a state transformer (or collection of state transformers), the axiomatic semantics is a set […]