Step 1: Understanding the Concept:
Recognition in international law is a process whereby a state acknowledges the existence of another state or government. This can be done individually by states or by a group of states through an international organization.
Step 2: Detailed Explanation:
- Express Recognition: A formal declaration or statement by one state recognizing another.
- Conditional Recognition: Recognition granted subject to the fulfillment of certain conditions by the new state.
- De-facto Recognition: A provisional recognition of a state's factual existence, often when the recognizing state has doubts about its stability or legitimacy.
- Collective Recognition: This occurs when a group of states collectively recognizes the existence of a new state. The admission of a new state into the United Nations is considered a prime example of collective recognition. When a state is admitted as a member under Article 4 of the UN Charter, it implies that a significant majority of the international community, acting through the organization, has recognized it as a sovereign state meeting the criteria for membership. While it doesn't compel individual member states who voted against admission to recognize the new state, it is a powerful form of collective acknowledgment.
Given the context of admission to the UN, "Collective recognition" is the most accurate and specific term.