The Vatican Council in 1870 infallibly stated that St. Peter HAS (not will have) perpetual successors.
The pertinent quotation is found in Denzinger #1825: Si quis ergo dixerit, non esse ex ipsius Christi domini institutione seu iure divino, ut beatus Petrus in primatu super universam ecclesiam habeat perpetuos successores; … anathema sit.”
Habeat = he has (present tense—subjunctive because it follows dixerit according to sequence of tenses). Future tense (he will have) = habebit. He must have = debeat habere. Habeat then equals has, not must have or will have.
Perpetuus, a, um:
• Cassell’s Latin-English and English-Latin Dictionary: (peto) continuous, uninterrupted, continual. I. a, of space, munitiones, Caes.; oratio, Cic; carmen, Hor.; b. of time, unbroken, continuing, lasting, perpetual; ignis Vestae perpetuus ac sempiternus, Cic; questiones, composed of a standing body of judges, Cic; interpetuum, for ever, Cic. II. universal, general; jus, Cic. (Also see) • Second Latin, Scanlon and Scanlon: perpetual, everlasting, unfailing; in perpetuum, forever.