that whether an investigation is criminal or not has no impact on whether a false statement made to a government official may be prosecuted under 18 U.S.C. § 1001. The district court sustained the government’s relevance objection as to Jimenez’s testimony that Agent Hays allegedly offered that she could return to Mexico without arrest. Jimenez contends that this testimony was relevant to show her state of mind. The government argues that this testimony was properly excluded as irrelevant. However, this evidence does appear to be admissible to impeach Agent Hays’s testimony that he made no such offer. Testimony that would tend to impeach the government’s main witness, if believed by the jury, is relevant and admissible. See United States v. Davis, 639 F.2d 239, 244-45 (5th Cir.1981) (<HOLDING>). This error was not of constitutional
holding that a trial court abused its discretion by excluding the testimony of an expert witness where the testimony would have been relevant to show that the defendant breached a duty of care holding that a district court did not abuse its discretion in excluding the testimony of a witness that was not highly probative holding that the district court exceeded its discretion in excluding testimony proffered to discredit the key government witness holding that the district court did not abuse its discretion in limiting testimony to only one witness where additional witnesses would have provided the same testimony holding trial court acted within its discretion in excluding expert testimony