# Preimage

### Some articles on preimage, preimages:

Interpretation (model Theory) - Definition
... and is a surjective map from a subset of Nn onto M such that the -preimage (more precisely the -preimage) of every set X ⊆ Mk definable in M by a first-order formula without parameters is ... To verify that the preimage of every definable (without parameters) set in N is definable in M (with or without parameters), it is sufficient to check the preimages of the following definable sets the ...
Image (mathematics) - Inverse Image
... "Preimage" redirects here ... attack on hash functions, see preimage attack ... The preimage or inverse image of a set B ⊆ Y under f is the subset of X defined by The inverse image of a singleton, denoted by f −1 or by f −1, is also called the fiber over y or the level set of y ...
Fiber (mathematics)
... Y is the inverse image (also known as the preimage) of the singleton {y} under f, that is, In various applications, this is also called The preimage of y under f, or the ... Note that this terminology usually refers to the preimages of subsets of Y thus, to refer to the fiber of y one generally would call it the preimage of the singleton {y} under f) The level set of y under ...
Preimage Theorem
... mathematics, particularly in differential topology, the preimage theorem is a theorem concerning the preimage of particular points in a manifold under the action of a smooth map ...
Interpretation (model Theory) - Example
... To see that it is an interpretation (without parameters), one needs to check the following preimages of definable sets in Q the preimage of Q is defined by the formula φ(x, y) given ...