# Dictionary Definition

indiscernible adj

1 difficult or impossible to perceive or discern;
"an indiscernible increase in temperature" [ant: discernible]

2 barely able to be perceived; "the transition
was almost indiscernible"; "an almost insensible change" [syn:
insensible, undetectable]

# User Contributed Dictionary

## English

### Adjective

en-adj more- Not capable of being discerned; of being perceived

# Extensive Definition

In mathematical
logic, indiscernibles are objects which cannot be distinguished
by any property
or relation
defined by a formula.
Usually only first-order
formulas are considered. For example, if is indiscernible, then for
each 2-ary formula K, we must have K(A, B) if and only if K(B, A)
if and only if K(C, A) if and only if K(A, C) if and only if K(B,
C) if and only if K(C, B).

It is also common to consider
"order-indiscernibles", which possess a total ordering, and satisfy
relations
dependent only on the relative order of the arguments. If the set
above were only order-indiscernible (and ordered alphabetically),
we would have K(A, B) if and only if K(A, C) if and only if K(B,
C), but not K(A, B) if and only if K(B, A).

Order-indiscernibles feature prominently in the
theory of Ramsey
cardinals, Erdős
cardinals, and Zero
sharp.

## See also

# Synonyms, Antonyms and Related Words

alike,
atomic, behind the
curtain, behind the scenes, camouflaged, concealed, corpuscular, disguised, embryonic, evanescent, germinal, granular, hidden, impalpable, imperceptible, imponderable, inappreciable, indistinct, indistinctive, indistinguishable,
infinitesimal,
insensible, intangible, interchangeable,
invisible, latent, microcosmic, microscopic, molecular, out of sight,
secret, sightless, standard, stereotyped, subatomic, submerged, tenuous, thin, ultramicroscopic,
unapparent, unappreciable, unbeheld, unbeholdable, undifferentiated,
undiscernible,
undiscriminated,
undistinguishable,
undistinguished,
uniform, unnoticed, unobservable, unobserved, unperceivable, unperceived, unrealized, unseeable, unseen, unviewed, unwitnessed, viewless, without
distinction