A jury found the defendant guilty of felony murder in violation of General Statutes (Rev. to 1977) § 53a-54c as a result of a death caused by arson in an apartment building at Newhall Street in New Haven which occurred on January 14,1977. In his appeal the *661defendant claims that the trial court erred: (1) in instructing the jury upon the import of the phrase “in furtherance of such crime” in our felony murder statute, § 53a-54c; (2) in refusing to submit to the jury the affirmative defense available to one charged with felony murder; and (3) in denying the defendant’s motion to exclude a witness as incompetent, in permitting that witness to invoke the privilege against self-incrimination, and in refusing to strike his testimony. We find no error.
At approximately 7 p.m. on January 14,1977, members of the New Haven fire department responded to an alarm at an apartment building on Newhall Street. They discovered smoke and flames concentrated primarily at the rear of the building. In an apartment on the second floor they came upon a man and a six month old child, Tashika Nelson, who were at the time of the fire the only occupants of the building. The child died on April 27, 1978,1 from the effects of smoke inhalation sustained during the fire.
Julian Taylor, the principal witness for the state, confessed to igniting the fire. He admitted his involvement after he returned to the building while the fire was in progress. Apparently his confession was motivated by his discovery that someone had been injured in the fire. He testified that the defendant, whose wife owned the building, had paid him to “torch” it, but had assured him that the building would be unoccupied at the agreed time. He had used gasoline to start the fire.
I
The defendant’s claim as to the significance of the phrase “in furtherance of such crime or flight there*662from” in our felony murder statute, § 53a-54c,2 is similar to that we have just rejected in State v. Young, 191 Conn. 636, 469 A.2d 1189 (1983). He argues that the phrase is intended to establish the requirement of a culpable state of mind with respect to a death occurring in the course of the felony in the form of an intention to cause the death or a reckless indifference to the likelihood of such a result. Since the evidence indicates not only a lack of such intention but a substantial effort by the defendant to ensure that no one would be in the building when the fire occurred, he contends that his motion for a judgment of acquittal should have been granted and also that the charge was erroneous in omitting the requirement of mens rea in respect to causing the death of the victim.
We concluded in Young that § 53a-54c contains no mens rea requirement beyond that of an intention to commit the underlying felony upon which the felony murder charge is predicated. We also held that the “in *663furtherance” phrase functions primarily as a limitation on the vicarious liability of an accomplice, such as the defendant in this case, who does not perform the homicidal act, and that, in some exceptional cases, it also serves to exclude murders occurring in the course of a felony which result from other causes. The trial court did not err in denying the defendant’s motion for an acquittal and in refusing his requests to modify the charge.
II
The refusal of the trial court to instruct the jury upon the affirmative defense to felony murder which the statute provides, as requested by the defendant, is also claimed as error. After defining the crime of felony murder, § 53a-54c makes the following exception: “except that in any prosecution under this section ... it shall be an affirmative defense that the defendant: (A) Did not commit the homicidal act or in any way solicit, request, command, importune, cause or aid the commission thereof; and (B) was not armed with a deadly weapon, or any dangerous instrument; and (C) had no reasonable ground to believe that any other participant was armed with such a weapon or instrument; and (D) had no reasonable ground to believe that any other participant intended to engage in conduct likely to result in death or serious physical injury.” An affirmative defense is one upon which the defendant has the burden of proof by a preponderance of the evidence. General Statutes § 53a-12. Since the four conditions which must be met to establish the affirmative defense created by § 53a-54c are stated conjunctively, the court was not obliged to submit this defense to the jury unless there was sufficient evidence to support a finding that each of those conditions had been proved by a fair preponderance of the evidence.
*664The defendant’s claim that this affirmative defense should have been submitted to the jury founders upon the first of these conditions: “(A) Did not commit the homicidal act or in any way solicit, request, command, importune, cause or aid the commission thereof. . . Under the circumstances of this case the “homicidal act” was the arson of the building which resulted in the death of a child.3 The state had the burden of proving the defendant’s complicity in that crime in accordance with the requirements of General Statutes § 53a-8, which imposes criminal liability for the acts of another upon a person who, “acting with the mental state required for commission of an offense . . . solicits, requests, commands, importunes or intentionally aids another person to engage in conduct which constitutes an offense.” The verdict of guilty which the jury rendered necessarily imports a finding beyond a reasonable doubt that the defendant did “solicit, request, command, importune, cause or aid” in the commission by Taylor of the underlying crime of arson which constituted the “homicidal act.” It would have been wholly illogical and utterly confusing for the court to instruct the jury that, after making such a finding, they should also decide whether the defendant had sustained his burden of proving that he was not involved in the arson as an accomplice in accordance with the defendant’s request. Where the “homicidal act” is the very crime alleged as the basis for accomplice liability, as in this case, it would be completely inappropriate to submit to a jury the affirmative defense to felony murder. This conclusion makes it unnecessary to consider whether there was sufficient evidence to support a finding that the three remaining conditions for that defense had been proved.
*665III
The defendant challenges the testimony of the state’s principal witness, Taylor, on two grounds: (1) that he was incompetent to testify as a witness; and (2) that he was allowed to invoke the privilege against self-incrimination improperly and thus to frustrate any cross-examination of him.
The defendant moved to exclude Taylor as a witness before he was permitted to testify. The court’s denial of this motion was well within the exercise of judicial discretion. “Because the competency of a witness is a matter peculiarly within the discretion of the trial court its ruling will be disturbed only in a clear case of an abuse or of some error in law.” State v. Brigandi, 186 Conn. 521, 534, 442 A.2d 927 (1982); State v. Stankowski, 184 Conn. 121, 139, 439 A.2d 918, cert. denied, 454 U.S. 1052, 102 S. Ct. 596, 70 L. Ed. 2d 588 (1981). The defendant refers to testimony of Taylor’s treatment for chronic alcoholism and drug abuse at several mental institutions, his extensive criminal record, and other evidence which might affect his credibility. None of this evidence would warrant our overturning the determination of competency made by the trial court.
The circumstances cited by the defendant in which Taylor invoked his privilege against self-incrimination involved primarily an incident on September 30,1978, in which he had been charged with shooting his former wife and in which he himself received two bullet wounds. During his cross-examination of Taylor the defendant inquired who had shot him, whether he had shot his wife, whether he had a gun in his possession at the time of the incident, and whether he had accused his wife of attempting to murder him. Taylor was also asked whether he had accused his wife of removing certain household goods from his home while he was *666hospitalized after the shooting incident, at what time he had married her, and whether he had concealed the true date of their marriage in order to obtain social security payments fraudulently. We are not persuaded that the invocation of the privilege was uncalled for with respect to the inquiries concerning the shooting incident, the false reports or the fraudulent social security payments. “The privilege afforded not only extends to answers that could in themselves support a conviction . . . but likewise embraces those which would furnish a link in the chain of evidence needed to prosecute . . . Hoffman v. United States, 341 U.S. 479, 486, 71 S. Ct. 814, 95 L. Ed. 1118 (1951); see Malloy v. Hogan, 378 U.S. 1, 12-13, 84 S. Ct. 1489, 12 L. Ed. 2d 653 (1964).
Even where the privilege is properly invoked it may become necessary to strike the testimony of a witness in order to preserve a defendant’s right of cross-examination. United States v. Seifert, 648 F.2d 557, 561 (9th Cir. 1980). It is clear, however, that the subjects upon which Taylor invoked the privilege were entirely collateral to the circumstances of the arson about which he had testified on direct examination. Much of the defendant’s cross-examination of him about such unrelated matters as the shooting incident seems to have been a highly questionable extension of the rule which permits attacking the credibility of a witness by utilizing specific acts of misconduct indicating untruthfulness. Martyn v. Donlin, 151 Conn. 402, 407-408, 198 A.2d 700 (1964); Shailer v. Bullock, 78 Conn. 65, 69-70, 61 A. 65 (1905).
The extreme sanction of striking the testimony of a witness should be resorted to only where the invocation of the privilege blocks inquiry into matters directly relating to the crime charged and not those which are merely collateral, such as the subjects of the cross-*667examination for credibility in this case. United States v. Seifert, supra, 561; Fountain v. United States, 384 F.2d 624, 627-28 (5th Cir. 1967), cert. denied sub nom. Marshall v. United States, 390 U.S. 1005, 88 S. Ct. 1246, 20 L. Ed. 2d 105 (1968). “Where the privilege has been invoked as to purely collateral matters, there is little danger of prejudice to the defendant and, therefore, the witness’s testimony may be used against him.” United States v. Cardillo, 316 F.2d 606, 611 (2d Cir.), cert. denied, 375 U.S. 822, 84 S. Ct. 60, 11 L. Ed. 2d 55 (1963).
We must also reject the claim of the defendant that Taylor, by voluntarily taking the witness stand, waived his privilege against self-incrimination. “Waiver can be inferred only hf (1) the witness' prior statements have created a significant likelihood that the finder of fact will be left with and prone to rely on a distorted view of the truth, and (2) the witness had reason to know that his prior statements would be interpreted as a waiver of the fifth amendment’s privilege against self-incrimination.’ ” State v. Altrui, 188 Conn. 161, 170, 448 A.2d 837 (1982), quoting Klein v. Harris, 667 F.2d 274, 287 (2d Cir. 1981). Neither of these conditions was fulfilled in this case, because the privilege was never invoked with respect to any inquiries relating to the commission of the crime or the defendant’s involvement in it, concerning which Taylor would be deemed to have waived the privilege. No such waiver can be implied for collateral matters related wholly to credibility. “The giving of testimony, whether by an accused or by any other witness, does not operate as a waiver of his privilege against self-incrimination when examined with respect to matters which relate only to credibility.” Fed. R. Evid. § 608 (b).
There is no error.
In this opinion Healey, Parskey and Grillo, Js., concurred.
The fact that the victim died more than a year and a day after the criminal act was the basis for a motion to dismiss the indictment, which the court denied. This ruling has not been challenged on appeal.
General Statutes (Rev. to 1977) § 53a-54c, at the time of the offense provided as follows:
“[General Statutes] Sec. 53a-54c. felony murder. A person is guilty of murder when acting either alone or with one or more persons, he commits or attempts to commit robbery, burglary, kidnapping, arson, sexual assault in the first degree, sexual assault in the first degree with a firearm, sexual assault in the third degree, sexual assault in the third degree with a firearm, escape in the first degree, or escape in the second degree and, in the course of and in furtherance of such crime or of flight therefrom, he, or another participant, if any, causes the death of a person other than one of the participants, except that in any prosecution under this section, in which the defendant was not the only participant in the underlying crime, it shall be an affirmative defense that the defendant: (A) Did not commit the homicidal act or in any way solicit, request, command, importune, cause or aid the commission thereof; and (B) was not armed with a deadly weapon, or any dangerous instrument; and (C) had no reasonable ground to believe that any other participant was armed with such a weapon or instrument; and (D) had no reasonable ground to believe that any other participant intended to engage in conduct likely to result in death or serious physical injury.”
The dissenting opinion is critical of our conclusion that the “homicidal act” was the arson, but fails to identify any other event which might have caused the homicide.