I Are there any examples of two large cardinal axioms AX and AY, in the language of first order ZFC, which satisfy the following conditions. (1) Each of them defines a unique cardinal number-C(AX) for AX and C(AY) for AY-not like the axiom of measurable cardinals wich defines a whole collection of cardinal numbers. (2) If T denotes the theory ZFC+AX+AY, then T has not yet been proved inconsistent. (3) T proves that each of C(AX) and C(AY) is larger that the smallest strongly inacessible cardinal number. (4) The sentences of T stating that C(AX)<C(AY) and that C(AY)<C(AX) are each consistent with T, if T is consistent.