Which Church teachings have been declared infallible?
I have had some heated discussions recently about what teachings of the Church have been formally defined as infallible. I believe that under the definition of infallibility set forth at the First Vatican Council and affirmed at the Second Vatican Council in Lumen Gentium, the following teachings have been infallibly taught: the Immaculate Conception, the Assumption, the reservation of priestly ordination to men, and the immorality of abortion and other deliberate killing of innocent persons. So, which teachings of the Church are in fact formally defined?
The Church has not yet compiled a list of all infallible teachings or dogmatic definitions. However, all of the teachings you name are infallible.
Some of them—the Immaculate Conception and the Assumption—have been infallibly taught by a definition of the extraordinary magisterium (i.e., in a definition of a pope or an ecumenical council). Others—the male priesthood, the intrinsic evil of abortion and the deliberate killing of innocents—are infallibly taught, without a definition, by the Church’s ordinary magisterium.
Tests for whether a definition has been made include: (a) if a pope is writing, does he use the phrase "I define"? and (b) if a council is writing, does it use the phrase "let him be anathema"? If either of these is the case, it’s probably an infallible definition, especially as this language has been used in recent centuries. There are other ways popes and councils can issue definitions, but these are phrases commonly used to do so.