After his conviction of murder in the first degree on the theory of extreme atrocity or cruelty was reversed and the case remanded for a new trial, see Commonwealth v. DePace, 433 Mass. 379 (2001), the defendant again was tried and convicted of murder in the first degree based on extreme atrocity or cruelty. On appeal he alleges error in the denial of his motion to dismiss the indictment for failure to specify the theories of murder in the first degree on which the grand jury determined the indictment would issue, and error in the exclusion of evidence of the reversal of his prior conviction in this case, which he contends was critical to his defense. We affirm the conviction and decline to grant relief under G. L. c. 278, § 33E.
Background. The defendant and the victim, his wife, Natalina, had lived in Waltham since 1975. They had two sons, Rocco and Nicola. The sons were close to their mother, but they had a strained relationship with the defendant. In the summer of 1990, the defendant vacationed alone in Italy. He visited Natalina’s sister, Anna, who lived in Brindisi, and told her that he and his wife were not getting along. He claimed that she was stealing money from him, and he was convinced that she had been unfaithful. He had made similar assertions to his sons.
Relations between the defendant and his wife deteriorated over the next six years. Convinced that she was unfaithful, he hired a private investigator to follow her. He told a friend that he only learned that she “is in bed by six o’clock sleeping like an angel.” In December, 1996, the defendant and Natalina discussed divorce. He told her he would agree to a divorce, but that he wanted her out of his house.
On December 24, 1996, the defendant again told Nicola that his mother had been stealing his money and lying, and that she had been unfaithful. He also accused her of sending money and antiques to her sisters in Italy. Nicola offered to help them get a divorce, and suggested an equal distribution of their assets. The defendant became furious, yelling that he did not intend to lose everything he had earned, and that he would never give Natalina the satisfaction of a divorce. He said, “I’m going to be forced to kill your mother and everyone will blame me and think it was my fault.” He then yelled, “Don’t be surprised if *741you find her run over by a car some morning. I’m going to teach you both a lesson that you will never forget.”
On Sunday, March 2, 1997, Nicola telephoned his mother at home. The defendant answered and said that she was asleep. Nicola said that he was planning to be home that Friday, March 7. On Wednesday, March 5, the defendant visited his brother (who also lived in Waltham) at work and gave him a paper bag containing $85,000 in cash. He asked his brother to put it in an appropriate place. On Thursday, March 6, Natalina and a coworker took a bus home after work. The bus arrived at Natalina’s stop shortly after 4 p.m. She was never again seen alive. She failed to report to work the next day, Friday, March 7, and she did not report to work on Saturday or Sunday, March 8 and 9, at a second job that she held.
Rocco telephoned home Saturday evening, March 8, 1997, from Italy, where he was working as a yacht captain. The defendant answered the call, so Rocco hung up. At approximately 11 a.m. on Sunday, March 9, 1997, Nicola and Ms girl friend arrived at the family home. Nicola found Ms mother on the basement floor, dead. There was no evidence of forced entry of the home.
Natalina had a deep penetrating wound beMnd her left ear, six “chop” wounds caused by a dull-edged instrument on the left side of her head, including one that bisected her ear, and tMee chop wounds on the right side of her forehead. Her lips were cut and bruised, and she had extensive bruising on her face and scalp, including a broken nose and two black eyes. The gold wedding band on her left hand was flattened and her ring finger was broken. The tip of the fourth finger of her right hand had been crushed and was hanging by a tissue tMead. There were defensive wounds on her hands and elbows, and a bmise on her right Mp. She also had been strangled. The forensic pathologist who performed the autopsy opined that Natalina died witMn minutes to at most one hour after receiving multiple blunt impact injuries and multiple incised chop wounds. All wounds were inflicted while she was alive. The pathologist further opined that, based on the condition of the body just prior to the autopsy on March 10, 1997, Natalina had been dead at least thirty-six hours, or before Sunday, March 9, and not more than four to five days.
*742The defendant was arrested in the early afternoon on Sunday, March 9, 1997, at a gasoline station in Burlington. During his booking, the defendant requested a bandaid, which he put on a three-quarter inch cut on his right hand ring finger. His left hand had a cut on the palm and scratches on the back side. His right hand had scratches on the back side, and a bruise on the palm in the vicinity of the thumb. He had no cuts or bandages on his hands on Thursday, March 6, 1997, according to a friend who studied karate and martial arts weaponry with the defendant. (The defendant held a third degree black belt in karate.) Execution of a search warrant for the defendant’s vehicle produced some adhesive tape and a receipt indicating that it was purchased at 4:33 p.m. on March 8, 1997, and some bandaids and a receipt indicating they were purchased at 9:07 a.m. on March 9.
Motion to dismiss. The defendant argues that his pretrial motion to dismiss should have been allowed. He claimed then, as he does now, that the indictment was insufficient because it failed to specify any theory of murder in the first degree on which the grand jury had found probable cause to indict; and correspondingly, that an indictment that merely alleges murder, without specifying one or more theories of murder in the first degree, permits a prosecution of murder no greater than murder in the second degree. His motion to dismiss also raised a double jeopardy issue that the defendant renews on appeal, namely, that where the petit jury had previously rejected a conviction of murder in the first degree under a theory of deliberate premeditation and where there is no way of knowing if that theory was the only theory on which the grand jury issued the indictment, the indictment must be dismissed.
The defendant’s reliance on Apprendi v. New Jersey, 530 U.S. 466 (2000), is misplaced. In that case, the Supreme Court held that the due process clause of the Fifth Amendment to the United States Constitution and the notice and jury trial guarantees of the Sixth Amendment to the United States Constitution, as made applicable to the States by the due process clause of the Fourteenth Amendment to the United States Constitution, requires that “[ojther than the fact of a prior conviction, any fact that increases the penalty for a crime *743beyond the prescribed statutory minimum must be submitted to a jury, and proved beyond a reasonable doubt.” Id. at 490. The Apprendi case was not concerned with the sufficiency of a grand jury indictment. Here, conformably with Apprendi, the question of the defendant’s guilt as to the murder of his wife with extreme atrocity or cruelty, a form of murder in the first degree, was submitted to the jury and the charge was proved beyond a reasonable doubt. The defendant does not contend otherwise.
The essence of the defendant’s argument is that he cannot be convicted of murder in the first degree because the indictment simply alleges murder, which, he contends, constitutes murder in the second degree. An indictment for murder in the first degree, he argues, must allege each theory of murder (i.e., felony-murder, deliberate premeditation, or extreme atrocity or cruelty) that the grand jury determined is supported by probable cause.
The indictment in this case is in the statutory form prescribed by G. L. c. 277, § 79. General Laws c. 277, § 79, authorizes the following language to be used in an indictment alleging murder in the first degree: “That A.B. did assault and beat C.D., with intent to murder him (by striking him over the head with an axe), and by such assault and beating did (kill and) murder C.D. (and the jurors further say that the defendant is guilty of murder in the second degree and not in the first degree). This may be added if murder in the first degree is not alleged(emphasis in original). The indictment here does not specify murder in the second degree. As such, it charges the crime of murder in the first degree, and will survive a motion to dismiss. See Commonwealth v. Baker, 368 Mass. 58, 77 (1975); Commonwealth v. Baker, 343 Mass. 162, 164 (1961).
The statutory form of an indictment alleging murder that is not self-limiting to murder in the second degree encompasses all theories of murder in the first degree and is sufficient to charge murder by whatever means it may have been committed. See Commonwealth v. Gunter, 427 Mass. 259, 274 (1998). It also encompasses lesser included offenses such as murder in the second degree and manslaughter. See, e.g., Commonwealth v. Guy, 441 Mass. 96, 108-109 (2004). We conclude that the indict*744ment charging the defendant with murder alleges the crime of murder in the first degree, and that it encompasses all theories of murder in the first degree, including murder by extreme atrocity or cruelty, the same theory on which the defendant was convicted.
The defendant’s argument that Commonwealth v. Quincy Q., 434 Mass. 859, 862-863 (2001), requires dismissal is unavailing. In that case we said that the juvenile’s motion to dismiss should have been allowed because the Commonwealth failed to present to the grand jury sufficient evidence to support the alleged offense. Here, the defendant did not challenge the sufficiency of the evidence presented to the grand jury. His challenge went to the face of the indictment.
The defendant’s double jeopardy argument also fails. The case was presented to the jury at the first trial on theories of deliberate premeditation and extreme atrocity or cruelty. The jury found that guilt had been proved under the second theory, but not the first. The defendant argues that because there is no way of knowing if the grand jury had indicted only on a theory of deliberate premeditation, the indictment must be dismissed.
We do not consider the thought process of grand jurors, as the defendant would have us do. Rather, we review the sufficiency of the evidence presented to a grand jury according to an objective standard of probable cause to arrest. See Commonwealth v. McCarthy, 385 Mass. 160, 163 (1982). See also Commonwealth v. Franco, 419 Mass. 635, 639 (1995). The defendant does not argue that the evidence presented to the grand jury was insufficient to establish probable cause that the defendant murdered his wife with extreme atrocity or cruelty, only that the indictment does not specifically indicate that the grand jury so found. It is not the function of the grand jury to specify either the theory or the degree of murder. See Commonwealth v. Noble, 429 Mass. 44, 48 (1999). The test he asks us to apply is not required, under any constitutional provision or by statute. As discussed above, an indictment for murder, with no limiting language, is an indictment for . murder in the first degree that encompasses all three theories of murder in the first degree. Commonwealth v. Gunter, supra at 274.
The motion to dismiss was properly denied.
*745Evidence of prior appellate proceedings. The defendant’s conviction was reversed on February 16, 2001. See Commonwealth v. DePace, 433 Mass. 379 (2001). On May 17, 2001, Sergeant David Stanley of the Waltham police department received a telephone call from Rocco DePace. He. went to the DePace home, where Rocco showed him a knife he had found in the master bedroom closet on the second floor. Stanley secured the knife and turned it over to Trooper David Burke, who arranged for testing of stains on the knife. Test results were negative for blood and finger prints. At the time of the initial investigation on March 9, 1997, the knife that Rocco discovered had not been discovered by police, and no murder weapon had been found. The defendant’s second trial began on April 23, 2002.
At the second trial, counsel sought to impeach Rocco with evidence that after the defendant’s conviction had been reversed, Rocco “discovered” the knife to help the Commonwealth retry and convict his father either out of hatred for his father, or to divert suspicion away from himself. With respect to the latter, the defendant stresses that Rocco’s presence in Italy at the time he claims to have telephoned his mother on March 8, 1997, was not corroborated by any telephone records, passports, or eyewitness testimony, and that Rocco had a financial interest in the defendant’s conviction. The defendant argues that the judge’s refusal to admit evidence of the prior reversal of his conviction and its temporal relation to Rocco’s discovery of the knife was an impermissible limitation on his right to cross-examine Rocco that went to the core of his defense.
The defendant relies on Commonwealth v. Vardinski, 438 Mass. 444 (2003), in which we reversed a conviction and ordered a new trial because the trial judge refused to allow the defendant to cross-examine a complaining witness in an armed robbery case with an exact version of the mugshot used to identify the defendant before trial. The judge ordered a redaction of that portion of the mugshot that described a prior bad act, namely, a pending firearms charge. The defendant also had offered to introduce a certificate indicating that the firearms charge had been nolle pressed. Id. at 447-448. His intended strategy was to suggest that the identification of his image by *746the sole witness to the crime had been impermissibly reinforced by the information on the mugshot concerning the pending firearms charge. We reversed the conviction because the judge’s ruling, although adhering to the case law concerning prior bad acts, completely deprived the defendant of a reasonable trial strategy. Id. at 451.
Here, in contrast to the Vardinski case, the defendant was not deprived of his opportunity to pursue a reasonable trial strategy. He was permitted thorough and aggressive cross-examination of Rocco regarding his financial incentive to see that the defendant was convicted, his bias against the defendant, and the timing of his finding of the knife. Although he was not permitted to show that Rocco’s discovery of the knife occurred approximately three months after the defendant’s conviction was set aside, he was permitted to show that it occurred four years after the police finished their investigation of the crime scene. See Commonwealth v. Evans, 439 Mass. 184, 188-189 (2003).
Unlike the case of Commonwealth v. Vardinski, supra, the defendant did not have an adequate means to offset the potential prejudice of the evidence he sought to introduce. Nor was the potential prejudice directed solely at himself such that he could strategically decide to accept the risk of that prejudice. His prior appellate proceedings resulted in a reversal, not because of the sufficiency of the evidence, but because of the admission in evidence of his postarrest and post-Miranda request for an attorney, in violation of Doyle v. Ohio, 426 U.S. 610, 619 (1976). See Commonwealth v. DePace, supra at 382-387. Indeed, by the defendant’s introduction of evidence of the prior conviction and reversal, the Commonwealth would have been placed in the untenable position of either recommitting a Doyle error or risking juror speculation that the court had found some unidentified weakness in the Commonwealth’s case. See Commonwealth v. Qualls, 440 Mass. 576, 584 (2003). The trial judge did not abuse her discretion in excluding evidence of the prior reversal of his conviction. Commonwealth v. Evans, supra.
Review under G. L. c. 278, § 33E. Based on the briefs, the oral argument, and our review of the entire record, we see no reason to exercise our power under G. L. c. 278, § 33E, to reduce the verdict or order a new trial. The evidence establishes *747beyond a reasonable doubt that the defendant dispatched his wife with brutal efficiency, consistent with a murder committed with extreme atrocity or cruelty.
Judgment affirmed.