Common axioms defined for binary relations.

- completeness
- weakly connected
- transitivity
- negative transitive
- reflexivity
- irreflixivity
- symmetric
- asymmetric
- anitsymmetric
- acyclic

axioms inconsistent => There exists x,y in X s.t. axioms do not hold

axioms not independent => a (strict) subset of the axioms => the axioms

The axiom of choice:

- given any set M there exists a "choice function" f s.t. f(A) in A subset of M forall nonempty A subset of M.

The axiom of choice is subtle and powerful.

source

jl@crush.caltech.edu index

qualitative_probability

representation_theorem

certainty_equivalent

measurement_theory

weighted_utility

random_variable

betweenness

horse_race

normative

positive

savage

order

chain

QP5

QP4

QP3

QP2

QP1

PA2

PA1

AA5

AA4

AA3

Ps

P7

P6

P5

P4

P3

P2

P1

J3