A true claim (see truth) is one where the evidence indicates that the claim describes reality. A false claim is one where the evidence indicates that the claim does not describe reality. An arbitrary claim is one lacking any evidence, which is therefore neither true nor false. Arbitrary claims are, strictly speaking, not part of epistemology since they are not derived from reason. However, they are treated under epistemology because outside Objectivism, they may be used as an invalid means of gaining knowledge (more typical, denying knowledge).
A common arbitrary claim would be a statement like "There might be a tiny moon orbiting Earth -- you don't know that there isn't". Arbitrary statements are invalid as part of reasoning, and are widely used in denying the possibility of certainty, typically by asserting that one does not know that the arbitrary claim is not false.
An arbitrary claim is one that, by its nature, is outside the province of evidence, i.e. it is a claim for which no evidence can ever be generated. For instance, the claim that god exists is arbitrary, because god is defined as a being beyond man's comprehension; that which man cannot comprehend can never be proved or disproved.
The assertion of an arbitrary claim proves nothing and creates no obligation to disprove it. It should simply be identified as arbitrary and ignored.