As one candidate declined Friday to enter the race to replace Mayor John DeStefano Jr., the field of candidates for the city’shighest position is nearly settled.

Probate judge Jack Keyes — who last month indicated interest in joining the race — announced in a Friday statement that he ultimately decided not to enter the contest. But even as Keyes exits public speculation, Hillhouse High School Principal Kermit Carolina, who has flirted with the idea of a run in recent months, could soon join the race.

“After long consideration, I am not going to run mayor. I love my current job and want to stay,” Keyes said in a press release. “I thank, greatly, the people who were kind to me, and will honor them always. This city is my home; I love it, and will hope to be part of its fabric.”

With Keyes’ decision not to run, four candidates remain officially in the race: Ward 10 Alderman Justin Elicker FES ’10 SOM ’10, State Rep. Gary Holder-Winfield, former city economic development director Henry Fernandez and plumber Sundiata Keitazulu. Board of Aldermen president Jorge Perez, who was rumored to have considered a run in the wake of DeStefano’s retirement announcement and was considered a likely favorite in the race had he chosen to do so, officially stated last month that he would not be joining the race.

Carolina, meanwhile, has talked about a potential candidacy in the past, going so far as to form an exploratory committee two weeks ago. When reached for comment Sunday afternoon, Carolina declined to comment on whether he will run for mayor.

Carolina’s exploratory committee held an event at the Elks Club Tuesday night. According to exploratory committee member Jack Paulishen, over 400 people showed up to the event that was promoted by word of mouth, as the committee does not have a social media presence or formal communications.

Paulishen added that the exploratory committee has worked to spread the idea that Carolina is considering a mayoral run and test whether Carolina would be a viable candidate in this fall’s race. He said that he has seen “overwhelming support” for the idea of Carolina’s campaign.

“I will say that there has been nothing that has come up that has led me to believe that [Carolina] is not going to be a viable candidate — everything has been positive,” Paulishen said. “[At the Elks Club event], you couldn’t get in the place — people were standing in hallways and standing outside — and things have turned out extraordinarily well.”

Elicker and Holder-Winfield have told the News that the entrance of new candidates will not change their strategies or their campaigns.

Carolina has committed to using the Democracy Fund, New Haven’s public funding system for mayoral races, if he chooses to run this fall, joining Elicker, Keitazulu and Holder-Winfield in their use of the system. Fernandez, meanwhile, has opted out of the system, arguing that his late entry into the race will preclude effective use of the Democracy Fund.

The Democratic primary will be held on September 10.