axiom
statement that is taken to be true
axiom schema of replacement
in set theory, the axiom schema that the image of a set under a definable class function is also a set
axiom of union
axiom stating that for any set x there is a set y whose elements are precisely the elements of the elements of x
Church's thesis
axiom in constructive mathematics stating that all total functions are computable
continuum hypothesis
hypothesis that no set has a cardinality between that of the integers and that of the real numbers
probability axioms
axioms that are relevant to the probability theory
closed-world assumption
formal-logic assumption that any statement that is not known to be true is false
independence of irrelevant alternatives
axiom of decision theory and various social sciences
limited principle of omniscience
weakening of the law of excluded middle in constructive mathematics
Veblen-Young axiom
axiom in projective geometry describing intersections of lines
open-world assumption
formal-logic assumption that the truth-value of a statement is independent of whether it is known by any single observer or agent to be true
universal causation
the proposition that everything in the universe has a cause and is thus an effect of that cause
separation axiom
axioms in topology defining notions of "separation"
axiom of global choice
axiom in set theory that asserts that every class of non-empty sets has a choice function
action axiom
axiom that embodies a criterion for describing action
prescriptivity
term used in meta-ethics to state that when an evaluative judgment or decision is made it must either prescribe or condemn
principle of complete induction
mathematical axiom
principle of explosion
theorem which states that any statement can be proven from a contradiction
axiom schema of specification
axiom schema
principle of bivalence
classical logic of two values, either true and false
well-ordering principle
Statement that all sets of positive numbers contains a least element
gluing axiom
property defining a sheaf
principle of excluded middle
logical principle stating that for every proposition, either it or its negation is true
completeness of the real numbers
concept in mathematics
axiom of empty set
statement in set theory that asserts that the empty set exists
axiom of empty set
statement in set theory that asserts that the empty set exists
axiom of reducibility
axiom in Russell's ramified theory of types
sure-thing principle
decision-theoretic principle that an agent who would take a certain action if event 𝐸 has occurred as well as if the negation of 𝐸 has occurred, should also take that same action if they know nothing about 𝐸
parallel postulate
axiom in Euclidean geometry
principle
guiding rule or inevitable consequence of something, such as the laws observed in nature
Archimedean property
the absence of infinitesimals in a mathematical system
Peripatetic axiom
Greek principle quoted by Thomas Aquinas
square principle
combinatorial principle asserting the existence of a cohering sequence of club sets so that no one (long) club set coheres with them all