Why should we put Gamma and be done with it? OK, then let's clarify the ambiguity. I propose we "work from precedents" and review similar statements at other city articles. (note the lack of boosterism in these examples):

Boston (Boston is also a featured article) - Founded in 1630, Boston is one of the oldest and most culturally significant cities in the United States, and is recognized as a global or world city.

Miami - The region's importance as an international financial and cultural center has elevated Miami to the status of world city; because of its cultural and linguistic ties to North, South, and Central America, and the Caribbean it is sometimes called "The Gateway of the Americas."

 I propose "Houston is recognized as a global or world city by the Globalization and World Cities Study Group & Network"